Nonlinear Analysis, ISSN 0362-546X, 09/2012, Volume 75, Issue 13, pp. 5270 - 5282

In this paper, we introduce strongly Lipschitz p-integral operators, strongly Lipschitzp-nuclear operators and Lipschitz p-nuclear operators. It is shown that...

Lipschitz [formula omitted]-summing operators | Lipschitz [formula omitted]-integral operators | Lipschitz [formula omitted]-nuclear operators | [formula omitted]-integral operators | [formula omitted]-nuclear operators | [formula omitted]-summing operators | p-summing operators | Lipschitz p-integral operators | Lipschitz p-summing operators | p-nuclear operators | Lipschitz p-nuclear operators | p-integral operators | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | Nuclear industry

Lipschitz [formula omitted]-summing operators | Lipschitz [formula omitted]-integral operators | Lipschitz [formula omitted]-nuclear operators | [formula omitted]-integral operators | [formula omitted]-nuclear operators | [formula omitted]-summing operators | p-summing operators | Lipschitz p-integral operators | Lipschitz p-summing operators | p-nuclear operators | Lipschitz p-nuclear operators | p-integral operators | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | Nuclear industry

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2015, Volume 423, Issue 2, pp. 1410 - 1426

We consider the space of molecules endowed with the transposed version of the Chevet–Saphar norm and we identify its dual space with the space of Lipschitz...

Strongly p-summing operators | Lipschitz [formula omitted]-summing operators | Lipschitz p-summing operators | Pietsch factorization | p-Summing operators | Lipschitz Cohen strongly p-summing operators | P-Summing operators | Lipschitz (p, r, s)-summing operators | Lipschitz (p,r,s)-summing operators | FREE BANACH-SPACES | MATHEMATICS | MATHEMATICS, APPLIED

Strongly p-summing operators | Lipschitz [formula omitted]-summing operators | Lipschitz p-summing operators | Pietsch factorization | p-Summing operators | Lipschitz Cohen strongly p-summing operators | P-Summing operators | Lipschitz (p, r, s)-summing operators | Lipschitz (p,r,s)-summing operators | FREE BANACH-SPACES | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 2, pp. 1115 - 1137

We introduce the notions of strongly Lipschitz (p,r,s)-nuclear operators and strongly Lipschitz (p,r,s)-integral operators. We develop a theory of strongly...

Lipschitz map | Strongly Lipschitz [formula omitted]-nuclear operators | Strongly Lipschitz [formula omitted]-integral operators | Lipschitz r-compact operators | Strongly Lipschitz (p,r,s)-integral operators | Strongly Lipschitz (p,r,s)-nuclear operators | MATHEMATICS | MATHEMATICS, APPLIED | P-SUMMING OPERATORS | Strongly Lipschitz (p, r, s)-nuclear operators | COMPACT-OPERATORS | BANACH IDEALS | Strongly Lipschitz (p, r, s)-integral operators | INTEGRAL OPERATORS

Lipschitz map | Strongly Lipschitz [formula omitted]-nuclear operators | Strongly Lipschitz [formula omitted]-integral operators | Lipschitz r-compact operators | Strongly Lipschitz (p,r,s)-integral operators | Strongly Lipschitz (p,r,s)-nuclear operators | MATHEMATICS | MATHEMATICS, APPLIED | P-SUMMING OPERATORS | Strongly Lipschitz (p, r, s)-nuclear operators | COMPACT-OPERATORS | BANACH IDEALS | Strongly Lipschitz (p, r, s)-integral operators | INTEGRAL OPERATORS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2008, Volume 255, Issue 4, pp. 940 - 993

We discuss existence, uniqueness, and space–time Hölder regularity for solutions of the parabolic stochastic evolution equation { d U ( t ) = ( A U ( t ) + F (...

[formula omitted]-Lipschitz functions | Parabolic stochastic evolution equations | γ-Radonifying operators | Stochastic convolutions | UMD Banach spaces | parabolic stochastic evolution equations | stochastic convolutions | y-radonifying operators | L2y-Lipschitz functions | Lipschitz functions | L-gamma-Lipschitz functions | MATHEMATICS | INTEGRATION | REGULARITY | FOURIER MULTIPLIER THEOREMS | gamma-radonifying operators

[formula omitted]-Lipschitz functions | Parabolic stochastic evolution equations | γ-Radonifying operators | Stochastic convolutions | UMD Banach spaces | parabolic stochastic evolution equations | stochastic convolutions | y-radonifying operators | L2y-Lipschitz functions | Lipschitz functions | L-gamma-Lipschitz functions | MATHEMATICS | INTEGRATION | REGULARITY | FOURIER MULTIPLIER THEOREMS | gamma-radonifying operators

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 06/2017, Volume 290, Issue 8-9, pp. 1347 - 1373

Building upon the results of M. C. Matos and extending previous work of J. D. Farmer, W. B. Johnson and J. A. Chávez‐Domínguez we define a Lipschitz mixed...

47J99 | 47L20 | operator ideal | 47H99 | 46T99 | domination theorem | 26A16 | Lipschitz summability maps | Lipschitz maps | MATHEMATICS | OPERATORS

47J99 | 47L20 | operator ideal | 47H99 | 46T99 | domination theorem | 26A16 | Lipschitz summability maps | Lipschitz maps | MATHEMATICS | OPERATORS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 6/2001, Volume 41, Issue 2, pp. 127 - 178

The explicit form of all possible variants of the Green formula is described for a boundary value problem when the “basic” operator is an arbitrary partial...

Mathematics | 35J25 | Analysis | 47A68 | 35J55 | MATHEMATICS | BOUNDARY-VALUE-PROBLEMS | MANIFOLDS | LIPSCHITZ-DOMAINS | BESOV | OPERATORS

Mathematics | 35J25 | Analysis | 47A68 | 35J55 | MATHEMATICS | BOUNDARY-VALUE-PROBLEMS | MANIFOLDS | LIPSCHITZ-DOMAINS | BESOV | OPERATORS

Journal Article

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A modified subgradient extragradient method for solving monotone variational inequalities

Journal of Inequalities and Applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 14

In the setting of Hilbert space, a modified subgradient extragradient method is proposed for solving Lipschitz-continuous and monotone variational inequalities...

subgradient extragradient method | Lipschitz-continuous mapping | convergence rate | variational inequalities | level set | half-spaces | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | MATHEMATICS | PROJECTION | WEAK-CONVERGENCE | HILBERT-SPACE | OPERATORS | Algorithms | Half spaces | Mathematical analysis | Inequalities | Texts | Projection | Hilbert space | Convergence | 47J20 | 90C30 | 90C52 | 90C25 | Research

subgradient extragradient method | Lipschitz-continuous mapping | convergence rate | variational inequalities | level set | half-spaces | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | MATHEMATICS | PROJECTION | WEAK-CONVERGENCE | HILBERT-SPACE | OPERATORS | Algorithms | Half spaces | Mathematical analysis | Inequalities | Texts | Projection | Hilbert space | Convergence | 47J20 | 90C30 | 90C52 | 90C25 | Research

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 12/2014, Volume 59, Issue 3, pp. 511 - 540

In this work we analyze a first order method especially tailored for smooth saddle point problems, based on an alternating extragradient scheme. The proposed...

Operations Research/Decision Theory | Convex and Discrete Geometry | Interior projection algorithm | Alternating extragradient method | Mathematics | Operations Research, Management Science | Smooth saddle point problem | Statistics, general | Non Euclidean distances | Optimization | MATHEMATICS, APPLIED | ALGORITHMS | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SUBGRADIENT METHODS | CONVERGENCE | OPTIMIZATION | OPERATORS | Analysis | Methods | Algorithms | Computer science | Studies | Lipschitz condition | Computation | Mathematical analysis | Saddle points | Texts | Projection | Convergence

Operations Research/Decision Theory | Convex and Discrete Geometry | Interior projection algorithm | Alternating extragradient method | Mathematics | Operations Research, Management Science | Smooth saddle point problem | Statistics, general | Non Euclidean distances | Optimization | MATHEMATICS, APPLIED | ALGORITHMS | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SUBGRADIENT METHODS | CONVERGENCE | OPTIMIZATION | OPERATORS | Analysis | Methods | Algorithms | Computer science | Studies | Lipschitz condition | Computation | Mathematical analysis | Saddle points | Texts | Projection | Convergence

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 05/2013, Volume 38, Issue 5, pp. 882 - 924

We show the existence of global weak solutions to a general class of kinetic models of homogeneous incompressible dilute polymers. The main new feature of the...

Maximal monotone graph | Lipschitz approximation of Bochner functions | Weak solution | Implicit constitutive theory | Long-time and large-data existence | Kinetic theory | Non-Newtonian fluids | Unsteady flow | Viscoelastic fluids | 35D05 | MATHEMATICS, APPLIED | APPROXIMATION | EQUATIONS | WELL-POSEDNESS | MATHEMATICS | 46E30 | 76Z99 | FLUIDS | UNSTEADY FLOWS | FENE-DUMBBELL MODEL | 76D03 | SHEAR-RATE | 35Q35 | SYSTEMS | MICRO | LOCAL EXISTENCE | Studies | Partial differential equations | Polymers | Approximations | Fluids | Approximation | Computational fluid dynamics | Images | Fluid flow | Mathematical models | Probability density functions

Maximal monotone graph | Lipschitz approximation of Bochner functions | Weak solution | Implicit constitutive theory | Long-time and large-data existence | Kinetic theory | Non-Newtonian fluids | Unsteady flow | Viscoelastic fluids | 35D05 | MATHEMATICS, APPLIED | APPROXIMATION | EQUATIONS | WELL-POSEDNESS | MATHEMATICS | 46E30 | 76Z99 | FLUIDS | UNSTEADY FLOWS | FENE-DUMBBELL MODEL | 76D03 | SHEAR-RATE | 35Q35 | SYSTEMS | MICRO | LOCAL EXISTENCE | Studies | Partial differential equations | Polymers | Approximations | Fluids | Approximation | Computational fluid dynamics | Images | Fluid flow | Mathematical models | Probability density functions

Journal Article

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Stability estimate in an inverse problem for non-autonomous magnetic Schrödinger equations

Applicable Analysis: Dedicated to Michael V. Klibanov, outstanding expert in inverse problems, ISSN 0003-6811, 10/2011, Volume 90, Issue 10, pp. 1499 - 1520

We consider the inverse problem of determining the time-dependent magnetic field of the Schrödinger equation in a bounded open subset of , , from a finite...

time-dependent Hamiltonian | inverse problem | Carleman estimate | Lipschitz stability estimate | Schrödinger equation | magnetic vector potential | Time-dependent hamiltonian | Magnetic vector potential | Inverse problem | SYSTEM | MATHEMATICS, APPLIED | Schrodinger equation | RECONSTRUCTION | LIPSCHITZ STABILITY | OPERATORS | UNIQUENESS | Coulomb friction | Inverse problems | Stability | Mathematical analysis | Images | Schroedinger equation | Boundaries | Magnetic fields

time-dependent Hamiltonian | inverse problem | Carleman estimate | Lipschitz stability estimate | Schrödinger equation | magnetic vector potential | Time-dependent hamiltonian | Magnetic vector potential | Inverse problem | SYSTEM | MATHEMATICS, APPLIED | Schrodinger equation | RECONSTRUCTION | LIPSCHITZ STABILITY | OPERATORS | UNIQUENESS | Coulomb friction | Inverse problems | Stability | Mathematical analysis | Images | Schroedinger equation | Boundaries | Magnetic fields

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2016, Volume 144, Issue 5, pp. 1867 - 1875

We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied...

Doubly substochastic matrices | Singular values | Functional calculus | Lipschitz estimates | MATHEMATICS | MATRIX | MATHEMATICS, APPLIED | functional calculus | doubly substochastic matrices | singular values | RANK | Mathematics - Functional Analysis

Doubly substochastic matrices | Singular values | Functional calculus | Lipschitz estimates | MATHEMATICS | MATRIX | MATHEMATICS, APPLIED | functional calculus | doubly substochastic matrices | singular values | RANK | Mathematics - Functional Analysis

Journal Article

Applicable Analysis, ISSN 0003-6811, 10/2019, Volume 98, Issue 13, pp. 2423 - 2439

In this paper, we revisit the numerical approach to variational inequality problems involving strongly monotone and Lipschitz continuous operators by a variant...

strongly monotone operator | Projection method | Variational inequality | Lipschitz continuity | COMMON SOLUTIONS | MATHEMATICS, APPLIED | GRADIENT METHODS | SUBGRADIENT EXTRAGRADIENT METHODS | CONVERGENCE | SYSTEMS | Operators | Algorithms | Convergence

strongly monotone operator | Projection method | Variational inequality | Lipschitz continuity | COMMON SOLUTIONS | MATHEMATICS, APPLIED | GRADIENT METHODS | SUBGRADIENT EXTRAGRADIENT METHODS | CONVERGENCE | SYSTEMS | Operators | Algorithms | Convergence

Journal Article

Siberian Mathematical Journal, ISSN 0037-4466, 5/2006, Volume 47, Issue 3, pp. 537 - 550

We give a complete description for the Lipschitzian superposition operators acting on mappings of finite Λ-variation with values in a metric semigroup or...

Banach algebra type property | Lipschitz condition | Waterman Λ-variation | Mathematics, general | Mathematics | Nemytskii superposition operator | mapping with values in a metric space | Mapping with values in a metric space

Banach algebra type property | Lipschitz condition | Waterman Λ-variation | Mathematics, general | Mathematics | Nemytskii superposition operator | mapping with values in a metric space | Mapping with values in a metric space

Journal Article

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The BEM with graded meshes for the electric field integral equation on polyhedral surfaces

Numerische Mathematik, ISSN 0029-599X, 4/2016, Volume 132, Issue 4, pp. 631 - 655

We consider the variational formulation of the electric field integral equation on a Lipschitz polyhedral surface $$\Gamma $$ Γ . We study the Galerkin...

78M15 | Mathematical Methods in Physics | 65N12 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65N38 | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | INTERPOLATION | MATHEMATICS, APPLIED | LIPSCHITZ POLYHEDRA | OPERATOR | BOUNDARY-ELEMENT METHODS | TRACES | ELECTROMAGNETIC SCATTERING | DOMAINS | NATURAL HP-BEM | MAXWELLS EQUATIONS | Anisotropy | Electric fields | Analysis

78M15 | Mathematical Methods in Physics | 65N12 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65N38 | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | INTERPOLATION | MATHEMATICS, APPLIED | LIPSCHITZ POLYHEDRA | OPERATOR | BOUNDARY-ELEMENT METHODS | TRACES | ELECTROMAGNETIC SCATTERING | DOMAINS | NATURAL HP-BEM | MAXWELLS EQUATIONS | Anisotropy | Electric fields | Analysis

Journal Article

Siberian Advances in Mathematics, ISSN 1055-1344, 4/2011, Volume 21, Issue 2, pp. 100 - 129

We obtain two new equivalent quasinorms for unweighted isotropic Besov and Lizorkin-Triebel spaces in the epigraph of a Lipschitz function. The question on the...

Lipschitz domain | composition operator | straightening | Lizorkin-Triebel space | Mathematics, general | Mathematics | superposition operator | Besov space

Lipschitz domain | composition operator | straightening | Lizorkin-Triebel space | Mathematics, general | Mathematics | superposition operator | Besov space

Journal Article

Milan Journal of Mathematics, ISSN 1424-9286, 12/2009, Volume 77, Issue 1, pp. 397 - 436

Let $${\Omega \subset \mathbb{R}^d}$$ be some bounded domain with reasonable boundary and let f be a continuous function on the complement Ω c . We can...

random walks | homogenization | Analysis | Mathematics, general | Dirichlet problem | Mathematics | finite differences | harmonic functions | Harmonic functions | Homogenization | Random walks | Finite differences | MATHEMATICS, APPLIED | THEOREM | EQUATIONS | POTENTIAL-THEORY | LIPSCHITZ-DOMAINS | CONICAL DOMAINS | MATHEMATICS | RANDOM-WALKS | OPERATORS

random walks | homogenization | Analysis | Mathematics, general | Dirichlet problem | Mathematics | finite differences | harmonic functions | Harmonic functions | Homogenization | Random walks | Finite differences | MATHEMATICS, APPLIED | THEOREM | EQUATIONS | POTENTIAL-THEORY | LIPSCHITZ-DOMAINS | CONICAL DOMAINS | MATHEMATICS | RANDOM-WALKS | OPERATORS

Journal Article

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 04/2014, Volume 58, Issue 1, pp. 231 - 253

We show results on L-p-spectral multipliers for Maxwell operators with bounded measurable coefficients. We also present similar results for the Stokes operator...

Stokes operator | Maxwell operator | Lamé system; Lipschitz domains | Hodge boundary conditions | spectral multipliers | SPACES | EQUATIONS | NONSMOOTH DOMAINS | Lipschitz domains | MATHEMATICS | SEMIGROUPS | MAXIMAL REGULARITY | Lame system | THEOREMS | INFINITY-FUNCTIONAL-CALCULUS | OPERATORS | RIEMANNIAN-MANIFOLDS | Boundary conditions | Mathematics

Stokes operator | Maxwell operator | Lamé system; Lipschitz domains | Hodge boundary conditions | spectral multipliers | SPACES | EQUATIONS | NONSMOOTH DOMAINS | Lipschitz domains | MATHEMATICS | SEMIGROUPS | MAXIMAL REGULARITY | Lame system | THEOREMS | INFINITY-FUNCTIONAL-CALCULUS | OPERATORS | RIEMANNIAN-MANIFOLDS | Boundary conditions | Mathematics

Journal Article

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Nonlinear Approximation Rates and Besov Regularity for Elliptic PDEs on Polyhedral Domains

Foundations of Computational Mathematics, ISSN 1615-3375, 2015, Volume 15, Issue 2, pp. 561 - 589

We investigate the Besov regularity for solutions of elliptic PDEs. This is based on regularity results in Babuska-Kondratiev spaces. Following the argument of...

Regularity for elliptic PDEs | Kondratiev spaces | n-Term approximation | Adaptive finite element approximation | Besov regularity | Wavelet decomposition | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | COMPUTER SCIENCE, THEORY & METHODS | LIPSCHITZ-DOMAINS | Differential equations, Partial | Analysis | Approximation theory | Nonlinear equations | Computational mathematics | Finite element analysis | Finite element method | Foundations | Approximation | Partial differential equations | Mathematical analysis | Texts | Nonlinearity | Mathematical models | Regularity

Regularity for elliptic PDEs | Kondratiev spaces | n-Term approximation | Adaptive finite element approximation | Besov regularity | Wavelet decomposition | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | COMPUTER SCIENCE, THEORY & METHODS | LIPSCHITZ-DOMAINS | Differential equations, Partial | Analysis | Approximation theory | Nonlinear equations | Computational mathematics | Finite element analysis | Finite element method | Foundations | Approximation | Partial differential equations | Mathematical analysis | Texts | Nonlinearity | Mathematical models | Regularity

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 1/2017, Volume 223, Issue 1, pp. 213 - 264

We develop a framework for a unified treatment of well-posedness for the Stefan problem with or without surface tension. In the absence of surface tension, we...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | ANALYTIC SOLUTIONS | WATER-WAVES | MATHEMATICS, APPLIED | MECHANICS | PHASE-TRANSITION PROBLEMS | GLOBAL EXISTENCE | MUSKAT PROBLEM | STABILITY | FREE-BOUNDARY | HELE-SHAW | LIPSCHITZ INITIAL DATA | EULER EQUATIONS | Surface tension | Well posed problems | Sobolev space | Velocity | Approximation | Mathematical analysis | Texts | Estimates | Regularity | Heat equations

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | ANALYTIC SOLUTIONS | WATER-WAVES | MATHEMATICS, APPLIED | MECHANICS | PHASE-TRANSITION PROBLEMS | GLOBAL EXISTENCE | MUSKAT PROBLEM | STABILITY | FREE-BOUNDARY | HELE-SHAW | LIPSCHITZ INITIAL DATA | EULER EQUATIONS | Surface tension | Well posed problems | Sobolev space | Velocity | Approximation | Mathematical analysis | Texts | Estimates | Regularity | Heat equations

Journal Article

Applied Mathematics & Optimization, ISSN 0095-4616, 10/2014, Volume 70, Issue 2, pp. 309 - 344

We deal with the $$2D$$ 2 D -Navier–Stokes system endowed with Cauchy boundary conditions, but with no initial condition. We assume that the right-hand side is...

Identification of a constant | Systems Theory, Control | Linear parabolic non-characteristic problem | 35R30 | Theoretical, Mathematical and Computational Physics | Uniqueness | Mathematics | Carleman estimates | 35Q30 | 76D07 | Navier–Stokes system | Mathematical Methods in Physics | Local in time Lipschitz continuous dependence | Calculus of Variations and Optimal Control; Optimization | Numerical and Computational Physics | 35R25 | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | EQUATIONS | Navier-Stokes system | LOCAL EXACT CONTROLLABILITY | Studies | Boundary conditions | Cauchy problems | Applied mathematics | Initial conditions | Mathematical analysis | Texts | Constants | Two dimensional | Optimization | Navier-Stokes equations

Identification of a constant | Systems Theory, Control | Linear parabolic non-characteristic problem | 35R30 | Theoretical, Mathematical and Computational Physics | Uniqueness | Mathematics | Carleman estimates | 35Q30 | 76D07 | Navier–Stokes system | Mathematical Methods in Physics | Local in time Lipschitz continuous dependence | Calculus of Variations and Optimal Control; Optimization | Numerical and Computational Physics | 35R25 | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | EQUATIONS | Navier-Stokes system | LOCAL EXACT CONTROLLABILITY | Studies | Boundary conditions | Cauchy problems | Applied mathematics | Initial conditions | Mathematical analysis | Texts | Constants | Two dimensional | Optimization | Navier-Stokes equations

Journal Article

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