The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 1/2010, Volume 40, Issue 5, pp. 1505 - 1525

We consider metric variants of homogeneity, countable dense homogeneity (CDH) and strong local homogeneity (SLH) by requiring that the homeomorphisms that...

Embeddings | Cantor set | Topological theorems | Mathematical theorems | Homeomorphism | Separable spaces | Mathematical functions | Metric spaces | Topological spaces | Countable dense homogeneous | Isometry | Strongly locally homogeneous | Bi-Lipschitz map | MATHEMATICS | HILBERT-CUBE | strongly locally homogeneous | SPACES | bi-Lipschitz map | isometry | 54E40 | 46B04

Embeddings | Cantor set | Topological theorems | Mathematical theorems | Homeomorphism | Separable spaces | Mathematical functions | Metric spaces | Topological spaces | Countable dense homogeneous | Isometry | Strongly locally homogeneous | Bi-Lipschitz map | MATHEMATICS | HILBERT-CUBE | strongly locally homogeneous | SPACES | bi-Lipschitz map | isometry | 54E40 | 46B04

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2020, Volume 486, Issue 1, p. 123839

The purpose of this article is to explore the very general phenomenon that a function between metric spaces has a particular metric property if and only if...

Locally Lipschitz function | Lipschitz spaces | Cauchy continuous function | Uniformly continuous function | Lipschitz in the small function | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | COMPLETENESS

Locally Lipschitz function | Lipschitz spaces | Cauchy continuous function | Uniformly continuous function | Lipschitz in the small function | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | COMPLETENESS

Journal Article

Optimization Letters, ISSN 1862-4472, 2/2019, Volume 13, Issue 1, pp. 163 - 174

In the recent paper of Giorgi et al. (J Optim Theory Appl 171:70–89, 2016), the authors introduced the so-called approximate Karush–Kuhn–Tucker (AKKT)...

Multiobjective optimization problems | Locally Lipschitz functions | Computational Intelligence | Mordukhovich subdifferential | Operations Research/Decision Theory | Mathematics | Numerical and Computational Physics, Simulation | Approximate optimality conditions | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Mathematics - Optimization and Control

Multiobjective optimization problems | Locally Lipschitz functions | Computational Intelligence | Mordukhovich subdifferential | Operations Research/Decision Theory | Mathematics | Numerical and Computational Physics, Simulation | Approximate optimality conditions | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Mathematics - Optimization and Control

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2018, Volume 171, Issue 1, pp. 463 - 487

In this paper we study local error bound moduli for a locally Lipschitz and regular function via outer limiting subdifferential sets. We show that the distance...

Outer limiting subdifferential | Theoretical, Mathematical and Computational Physics | End set | Mathematics | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Locally Lipschitz | Numerical Analysis | 90C34 | Lower $${\mathcal {C}}^1$$ C 1 function | Support function | 65K10 | Combinatorics | Error bound modulus | Lower C | function | LOWER SEMICONTINUOUS FUNCTIONS | MATHEMATICS, APPLIED | CALMNESS | WEAK SHARP MINIMA | SUFFICIENT CONDITIONS | STABILITY | Lower C-1 function | CONSTRAINT QUALIFICATIONS | CONVEX INEQUALITIES | METRIC REGULARITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BANACH-SPACES | LINEAR INEQUALITY SYSTEMS | Error analysis | Constraining

Outer limiting subdifferential | Theoretical, Mathematical and Computational Physics | End set | Mathematics | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Locally Lipschitz | Numerical Analysis | 90C34 | Lower $${\mathcal {C}}^1$$ C 1 function | Support function | 65K10 | Combinatorics | Error bound modulus | Lower C | function | LOWER SEMICONTINUOUS FUNCTIONS | MATHEMATICS, APPLIED | CALMNESS | WEAK SHARP MINIMA | SUFFICIENT CONDITIONS | STABILITY | Lower C-1 function | CONSTRAINT QUALIFICATIONS | CONVEX INEQUALITIES | METRIC REGULARITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BANACH-SPACES | LINEAR INEQUALITY SYSTEMS | Error analysis | Constraining

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 12/2007, Volume 17, Issue 4, pp. 593 - 647

In the first part of this article we give intrinsic characterizations of the classes of Lipschitz and C1 domains. Under some mild, necessary, background...

secondary: 26A16, 26A66, 26B30 | Mathematics | Locally strongly Lipschitz domains | C 1 domains | bi-Lipschitz maps | transversal fields | Abstract Harmonic Analysis | surface area | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | C 1 diffeomorphisms | Primary: 49Q15, 26B15, 49Q25 | Differential Geometry | Dynamical Systems and Ergodic Theory | sets of locally finite perimeter | unit normal | MATHEMATICS | locally strongly Lipschitz domains | REGULARITY | DIRICHLET PROBLEM | C-1 diffeomorphisms | C-1 domains

secondary: 26A16, 26A66, 26B30 | Mathematics | Locally strongly Lipschitz domains | C 1 domains | bi-Lipschitz maps | transversal fields | Abstract Harmonic Analysis | surface area | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | C 1 diffeomorphisms | Primary: 49Q15, 26B15, 49Q25 | Differential Geometry | Dynamical Systems and Ergodic Theory | sets of locally finite perimeter | unit normal | MATHEMATICS | locally strongly Lipschitz domains | REGULARITY | DIRICHLET PROBLEM | C-1 diffeomorphisms | C-1 domains

Journal Article

Advances in Operator Theory, 12/2017, Volume 2, Issue 1, pp. 21 - 49

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 8/2019, Volume 189, Issue 4, pp. 595 - 609

We introduce the notion of Lipschitz p-compact operators. We show that they can be seen as a natural extension of the linear p-compact operators of Sinha and...

Lipschitz operators | Primary 47B07 | Secondary 26A16 | 47L20 | Lipschitz p -compact operators | 47B10 | Mathematics, general | Mathematics | Locally p -compact mappings | Lipschitz-free p -compact mappings | Lipschitz-free p-compact mappings | Lipschitz p-compact operators | Locally p-compact mappings | MATHEMATICS | NUCLEAR | ADJOINTS | OPERATORS | IDEALS

Lipschitz operators | Primary 47B07 | Secondary 26A16 | 47L20 | Lipschitz p -compact operators | 47B10 | Mathematics, general | Mathematics | Locally p -compact mappings | Lipschitz-free p -compact mappings | Lipschitz-free p-compact mappings | Lipschitz p-compact operators | Locally p-compact mappings | MATHEMATICS | NUCLEAR | ADJOINTS | OPERATORS | IDEALS

Journal Article

Stochastics, ISSN 1744-2508, 04/2020, Volume 92, Issue 3, pp. 418 - 453

We investigate conditions for solvability and Malliavin differentiability of backward stochastic differential equations driven by a Lévy process. In...

Malliavin differentiability of BSDEs | BSDEs with jumps | quadratic BSDEs | existence and uniqueness of solutions to BSDEs | locally Lipschitz generator

Malliavin differentiability of BSDEs | BSDEs with jumps | quadratic BSDEs | existence and uniqueness of solutions to BSDEs | locally Lipschitz generator

Journal Article

9.
Full Text
Fine properties of Newtonian functions and the Sobolev capacity on metric measure spaces

Revista Matematica Iberoamericana, ISSN 0213-2230, 2016, Volume 32, Issue 1, pp. 219 - 255

Newtonian spaces generalize first-order Sobolev spaces to abstract metric measure spaces. In this paper, we study regularity of Newtonian functions based on...

Poincaŕe inequality | Banach function lattice | Newtonian space | Quasi-continuity | Sobolev capacity | Locally Lipschitz function | Continuity | Sobolev-type space | Metric measure space | Outer capacity | Doubling measure | doubling measure | outer capacity | metric measure space | INEQUALITY | continuity | LIPSCHITZ FUNCTIONS | locally Lipschitz function | EQUIVALENCE | DENSITY | MATHEMATICS | quasi-continuity | Poincare inequality | DERIVATIVES | GRADIENTS | Mathematics - Functional Analysis

Poincaŕe inequality | Banach function lattice | Newtonian space | Quasi-continuity | Sobolev capacity | Locally Lipschitz function | Continuity | Sobolev-type space | Metric measure space | Outer capacity | Doubling measure | doubling measure | outer capacity | metric measure space | INEQUALITY | continuity | LIPSCHITZ FUNCTIONS | locally Lipschitz function | EQUIVALENCE | DENSITY | MATHEMATICS | quasi-continuity | Poincare inequality | DERIVATIVES | GRADIENTS | Mathematics - Functional Analysis

Journal Article

10.
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About the existence of locally Lipschitz output feedback stabilizers for nonlinear systems

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2009, Volume 48, Issue 5, pp. 3389 - 3402

In this paper we complement some results of [L. Marconi, L. Praly, and A. Isidori, SIAM J. Control Optim., 45 (2007), pp. 2277-2298] by presenting a sufficient...

Locally lipschitz regulators | Robust control | Nonlinear observers | Nonlinear output regulation | Output stabilization | output stabilization | nonlinear output regulation | MATHEMATICS, APPLIED | locally Lipschitz regulators | robust control | nonlinear observers | AUTOMATION & CONTROL SYSTEMS | Studies | Control theory | Nonlinear systems | Convergence | Engineering Sciences | Automatic

Locally lipschitz regulators | Robust control | Nonlinear observers | Nonlinear output regulation | Output stabilization | output stabilization | nonlinear output regulation | MATHEMATICS, APPLIED | locally Lipschitz regulators | robust control | nonlinear observers | AUTOMATION & CONTROL SYSTEMS | Studies | Control theory | Nonlinear systems | Convergence | Engineering Sciences | Automatic

Journal Article

IET Control Theory & Applications, ISSN 1751-8644, 10/2015, Volume 9, Issue 16, pp. 2348 - 2356

This study discusses a linear matrix inequality (LMI)-based observer design for locally Lipschitz non-linear systems that ensures an ellipsoidal region of...

Research Articles | state estimation error | DESIGN | locally Lipschitz nonlinear systems | asymptotic stability | ellipsoidal Lipschitz region | ORDER | linear matrix inequalities | control nonlinearities | linear matrix inequality-based observer design | quadratic Lyapunov function analysis | multiple design objectives | AUTOMATION & CONTROL SYSTEMS | numerical simulations | EXPONENTIAL STABILITY | stabilisation controller design | control system synthesis | regional observer synthesis | LMI | TIME-DELAY | ENGINEERING, ELECTRICAL & ELECTRONIC | ROBUST-CONTROL | LMI APPROACH | SYNCHRONIZATION | INSTRUMENTS & INSTRUMENTATION | nonlinear control systems | dynamical nonlinearity | state feedback stabilisation scheme | state feedback | local exponential L-2 stability | local robust observer synthesis methodology | DESCRIPTOR SYSTEMS | observers | Lyapunov methods | ellipsoidal stability region | Nonlinear dynamics | Design engineering | State feedback | Synthesis | Stability | Methodology | Asymptotic properties | Dynamical systems

Research Articles | state estimation error | DESIGN | locally Lipschitz nonlinear systems | asymptotic stability | ellipsoidal Lipschitz region | ORDER | linear matrix inequalities | control nonlinearities | linear matrix inequality-based observer design | quadratic Lyapunov function analysis | multiple design objectives | AUTOMATION & CONTROL SYSTEMS | numerical simulations | EXPONENTIAL STABILITY | stabilisation controller design | control system synthesis | regional observer synthesis | LMI | TIME-DELAY | ENGINEERING, ELECTRICAL & ELECTRONIC | ROBUST-CONTROL | LMI APPROACH | SYNCHRONIZATION | INSTRUMENTS & INSTRUMENTATION | nonlinear control systems | dynamical nonlinearity | state feedback stabilisation scheme | state feedback | local exponential L-2 stability | local robust observer synthesis methodology | DESCRIPTOR SYSTEMS | observers | Lyapunov methods | ellipsoidal stability region | Nonlinear dynamics | Design engineering | State feedback | Synthesis | Stability | Methodology | Asymptotic properties | Dynamical systems

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2017, Volume 456, Issue 2, pp. 1013 - 1039

In this paper we introduce a realcompactification for any metric space (X,d), defined by means of the family of all its real-valued uniformly continuous...

Real-valued uniformly continuous functions | Samuel realcompactification | Bourbaki-completeness | Lipschitz realcompactification | Uniform Katětov–Shirota result | Bourbaki-boundedness | MATHEMATICS | Uniform Katetov-Shirota result | MATHEMATICS, APPLIED | LOCALLY LIPSCHITZ FUNCTIONS | UNIFORM-SPACES | UC SPACES | COMPLETENESS | Mathematics - General Topology

Real-valued uniformly continuous functions | Samuel realcompactification | Bourbaki-completeness | Lipschitz realcompactification | Uniform Katětov–Shirota result | Bourbaki-boundedness | MATHEMATICS | Uniform Katetov-Shirota result | MATHEMATICS, APPLIED | LOCALLY LIPSCHITZ FUNCTIONS | UNIFORM-SPACES | UC SPACES | COMPLETENESS | Mathematics - General Topology

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2018, Volume 334, pp. 39 - 57

We consider the use of adaptive timestepping to allow a strong explicit Euler–Maruyama discretisation to reproduce dynamical properties of a class of nonlinear...

A.s. stability and instability | Adaptive timestepping | Euler–Maruyama method | Locally Lipschitz coefficients | Positivity | Euler-Maruyama method | MATHEMATICS, APPLIED | INSTABILITY | APPROXIMATIONS | STABILIZATION | NOISE | EQUILIBRIUM | SDES | CONVERGENCE | LIPSCHITZ CONTINUOUS COEFFICIENTS

A.s. stability and instability | Adaptive timestepping | Euler–Maruyama method | Locally Lipschitz coefficients | Positivity | Euler-Maruyama method | MATHEMATICS, APPLIED | INSTABILITY | APPROXIMATIONS | STABILIZATION | NOISE | EQUILIBRIUM | SDES | CONVERGENCE | LIPSCHITZ CONTINUOUS COEFFICIENTS

Journal Article

Quarterly Journal of Mathematics, ISSN 0033-5606, 03/2011, Volume 62, Issue 1, pp. 39 - 58

Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for approximate amenability...

MATHEMATICS | SEMIGROUP ALGEBRAS | WEAK AMENABILITY | PSEUDO-AMENABILITY | LOCALLY COMPACT GROUP | BANACH-ALGEBRAS | GENERALIZED NOTIONS | Mathematics - Functional Analysis

MATHEMATICS | SEMIGROUP ALGEBRAS | WEAK AMENABILITY | PSEUDO-AMENABILITY | LOCALLY COMPACT GROUP | BANACH-ALGEBRAS | GENERALIZED NOTIONS | Mathematics - Functional Analysis

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 10/2009, Volume 143, Issue 1, pp. 87 - 105

The present paper studies the following constrained vector optimization problem: min (C) f(x), g(x)aa'K, h(x)=0, where f:a"e (n) -> a"e (m) , g:a"e (n) -> a"e...

Locally Lipschitz optimization | Optimality conditions | Dini derivatives | Vector optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Mathematical optimization | Analysis | Studies | Optimization

Locally Lipschitz optimization | Optimality conditions | Dini derivatives | Vector optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Mathematical optimization | Analysis | Studies | Optimization

Journal Article

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 05/2020, Volume 185, Issue 2, pp. 522 - 539

We extend some results of nonsmooth analysis from the Euclidean context to the Riemannian setting. Particularly, we discuss the concepts and some properties,...

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Semismooth vector field | NONSMOOTH OPTIMIZATION | Locally Lipschitz continuous vector fields | CONVERGENCE | SMOOTH | Riemannian manifold | Regularity | Newton method | Clarke generalized covariant derivative | Riemann manifold | Fields (mathematics) | Nonlinear programming | Singularities | Newton methods

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Semismooth vector field | NONSMOOTH OPTIMIZATION | Locally Lipschitz continuous vector fields | CONVERGENCE | SMOOTH | Riemannian manifold | Regularity | Newton method | Clarke generalized covariant derivative | Riemann manifold | Fields (mathematics) | Nonlinear programming | Singularities | Newton methods

Journal Article

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, 04/2020, Volume 114, Issue 3

This article provides necessary and sufficient conditions on the structure of a metric space such that for various vector lattices of real-valued...

Reciprocation | MATHEMATICS | Pointwise product | Cofinal completeness | Cauchy-Lipschitz function | Lipschitz in the small function | Lipschitz function | Locally Lipschitz function | COMPLETENESS | Modulus of continuity | UC-space | Metric space | Lattices | Continuity (mathematics)

Reciprocation | MATHEMATICS | Pointwise product | Cofinal completeness | Cauchy-Lipschitz function | Lipschitz in the small function | Lipschitz function | Locally Lipschitz function | COMPLETENESS | Modulus of continuity | UC-space | Metric space | Lattices | Continuity (mathematics)

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 12/2006, Volume 131, Issue 3, pp. 429 - 452

This study is devoted to constraint qualifications and Kuhn-Tucker type necessary optimality conditions for nonsmooth optimization problems involving locally...

Mathematics | Theory of Computation | necessary optimality conditions | Optimization | convexificators | Locally Lipschitz functions | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Dini derivatives | nonsmooth optimizations | Engineering, general | Applications of Mathematics | constraint qualifications | Necessary optimality conditions | Convexificators | Constraint qualifications | Nonsmooth optimizations | MATHEMATICS, APPLIED | MULTIOBJECTIVE OPTIMIZATION | LAGRANGE MULTIPLIERS | PROGRAMMING-PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | locally Lipschitz functions | MATRICES | BOUNDED MULTIPLIERS | EQUALITY | NONSMOOTH CALCULUS | TANGENT CONE | RULE | Studies | Tools | Minimization | Inequalities

Mathematics | Theory of Computation | necessary optimality conditions | Optimization | convexificators | Locally Lipschitz functions | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Dini derivatives | nonsmooth optimizations | Engineering, general | Applications of Mathematics | constraint qualifications | Necessary optimality conditions | Convexificators | Constraint qualifications | Nonsmooth optimizations | MATHEMATICS, APPLIED | MULTIOBJECTIVE OPTIMIZATION | LAGRANGE MULTIPLIERS | PROGRAMMING-PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | locally Lipschitz functions | MATRICES | BOUNDED MULTIPLIERS | EQUALITY | NONSMOOTH CALCULUS | TANGENT CONE | RULE | Studies | Tools | Minimization | Inequalities

Journal Article

19.
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A stable numerical scheme for stochastic differential equations with multiplicative noise

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2017, Volume 55, Issue 4, pp. 1614 - 1649

We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called the direction and...

Weak error | Locally Lipschitz SDEs | Mean-square convergence | Unstable equilibrium point | Rate of convergence | Stable numerical scheme | Bilinear SDEs | Stochastic differential equation | MATHEMATICS, APPLIED | MARUYAMA METHOD | LINEAR-STABILITY ANALYSIS | EXPONENTIAL STABILITY | unstable equilibrium point | locally Lipschitz SDEs | rate of convergence | DIFFUSION-COEFFICIENTS | MEAN-SQUARE | weak error | BALANCED IMPLICIT METHODS | LOCAL LINEARIZATION SCHEME | mean-square convergence | stochastic differential equation | ASYMPTOTIC STABILITY | stable numerical scheme | bilinear SDEs | LIPSCHITZ CONTINUOUS COEFFICIENTS | STRONG-CONVERGENCE

Weak error | Locally Lipschitz SDEs | Mean-square convergence | Unstable equilibrium point | Rate of convergence | Stable numerical scheme | Bilinear SDEs | Stochastic differential equation | MATHEMATICS, APPLIED | MARUYAMA METHOD | LINEAR-STABILITY ANALYSIS | EXPONENTIAL STABILITY | unstable equilibrium point | locally Lipschitz SDEs | rate of convergence | DIFFUSION-COEFFICIENTS | MEAN-SQUARE | weak error | BALANCED IMPLICIT METHODS | LOCAL LINEARIZATION SCHEME | mean-square convergence | stochastic differential equation | ASYMPTOTIC STABILITY | stable numerical scheme | bilinear SDEs | LIPSCHITZ CONTINUOUS COEFFICIENTS | STRONG-CONVERGENCE

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 6/2016, Volume 67, Issue 3, pp. 1 - 23

In this paper, we prove the existence of variational solutions to systems modeling electrorheological fluids in the stationary case. Our method of proof is...

Engineering | 35J20 | Mathematical Methods in Physics | Electrorheological fluids | Locally Lipschitz functional | Nonsmooth critical point theory | Theoretical and Applied Mechanics | 35J25 | MATHEMATICS, APPLIED | 3 NONTRIVIAL SOLUTIONS | MULTIPLE SOLUTIONS | HEMIVARIATIONAL INEQUALITIES | P(X)-LAPLACIAN EQUATIONS | LOCALIZATION PROPERTIES | R-N | SOBOLEV EMBEDDINGS | VARIABLE EXPONENT | ELLIPTIC-EQUATIONS | NONLINEAR DEGENERATE PROBLEM | Applications of mathematics | Mathematical models | Modelling | Critical point | Proving

Engineering | 35J20 | Mathematical Methods in Physics | Electrorheological fluids | Locally Lipschitz functional | Nonsmooth critical point theory | Theoretical and Applied Mechanics | 35J25 | MATHEMATICS, APPLIED | 3 NONTRIVIAL SOLUTIONS | MULTIPLE SOLUTIONS | HEMIVARIATIONAL INEQUALITIES | P(X)-LAPLACIAN EQUATIONS | LOCALIZATION PROPERTIES | R-N | SOBOLEV EMBEDDINGS | VARIABLE EXPONENT | ELLIPTIC-EQUATIONS | NONLINEAR DEGENERATE PROBLEM | Applications of mathematics | Mathematical models | Modelling | Critical point | Proving

Journal Article

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