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 Computational and Applied Mathematics, ISSN 0377-0427, 2008, Volume 211, Issue 1, pp. 90 - 102

In this paper, we modify the adaptive wavelet algorithm from Gantumur et al. [An optimal adaptive wavelet method without coarsening of the iterands, Technical...

Wavelets | Strongly elliptic operators | Adaptive methods | Optimal computational complexity | Best [formula omitted]-term approximation | Best N-term approximation | MATHEMATICS, APPLIED | optimal computational complexity | ELEMENT METHOD | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | LIPSCHITZ-DOMAINS | strongly elliptic operators | DOMAIN DECOMPOSITION | best N-term approximation | wavelets | CONSTRUCTION | BESOV REGULARITY | CONVERGENCE | COMPUTATION | INTEGRAL-OPERATORS | adaptive methods

Wavelets | Strongly elliptic operators | Adaptive methods | Optimal computational complexity | Best [formula omitted]-term approximation | Best N-term approximation | MATHEMATICS, APPLIED | optimal computational complexity | ELEMENT METHOD | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | LIPSCHITZ-DOMAINS | strongly elliptic operators | DOMAIN DECOMPOSITION | best N-term approximation | wavelets | CONSTRUCTION | BESOV REGULARITY | CONVERGENCE | COMPUTATION | INTEGRAL-OPERATORS | adaptive methods

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2014, Volume 57, Issue 5, pp. 903 - 962

We establish the theory of Orlicz-Hardy spaces generated by a wide class of functions.The class will be wider than the class of all the N-functions.In...

空间理论 | Hardy空间 | 有界性 | 对偶 | 原子分解 | N-函数 | 允许函数 | 生成子 | atomic decomposition | 42B35 | 42B30 | 46E30 | bounded mean oscillation | Campanato space | Mathematics | Orlicz space | Applications of Mathematics | Hardy space | MATHEMATICS, APPLIED | STRONGLY LIPSCHITZ-DOMAINS | INEQUALITIES | REAL-VARIABLE CHARACTERIZATIONS | LITTLEWOOD-PALEY THEORY | CAMPANATO SPACES | FRACTIONAL-INTEGRATION | MATHEMATICS | JACOBIANS | MORREY SPACES | OPERATORS | Functions (mathematics) | Operators | Infinity | Integrals | Mathematical analysis | China | Transforms | Texts

空间理论 | Hardy空间 | 有界性 | 对偶 | 原子分解 | N-函数 | 允许函数 | 生成子 | atomic decomposition | 42B35 | 42B30 | 46E30 | bounded mean oscillation | Campanato space | Mathematics | Orlicz space | Applications of Mathematics | Hardy space | MATHEMATICS, APPLIED | STRONGLY LIPSCHITZ-DOMAINS | INEQUALITIES | REAL-VARIABLE CHARACTERIZATIONS | LITTLEWOOD-PALEY THEORY | CAMPANATO SPACES | FRACTIONAL-INTEGRATION | MATHEMATICS | JACOBIANS | MORREY SPACES | OPERATORS | Functions (mathematics) | Operators | Infinity | Integrals | Mathematical analysis | China | Transforms | Texts

Journal Article

Functional Analysis and Its Applications, ISSN 0016-2663, 3/2011, Volume 45, Issue 2, pp. 81 - 98

We consider mixed problems for strongly elliptic second-order systems in a bounded domain with Lipschitz boundary in the space ℝ n . For such problems,...

potential type operator | Functional Analysis | Analysis | strongly elliptic system | eigenvalue asymptotics | Mathematics | mixed problem | spectral problem | MATHEMATICS, APPLIED | BESOV-SPACES | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | SPECTRAL ASYMPTOTICS | MATHEMATICS | REGULARITY | POISSON PROBLEM | VARIATIONAL-PROBLEMS | POTENTIAL TYPE OPERATORS | INTEGRAL-OPERATORS | RIEMANNIAN-MANIFOLDS

potential type operator | Functional Analysis | Analysis | strongly elliptic system | eigenvalue asymptotics | Mathematics | mixed problem | spectral problem | MATHEMATICS, APPLIED | BESOV-SPACES | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | SPECTRAL ASYMPTOTICS | MATHEMATICS | REGULARITY | POISSON PROBLEM | VARIATIONAL-PROBLEMS | POTENTIAL TYPE OPERATORS | INTEGRAL-OPERATORS | RIEMANNIAN-MANIFOLDS

Journal Article

5.
Full Text
Regularity for Inhomogeneous Dirichlet Problems of Some Schrödinger Equations on Domains

The Journal of Geometric Analysis, ISSN 1050-6926, 7/2016, Volume 26, Issue 3, pp. 2097 - 2129

Let $$n\ge 3, \Omega $$ n ≥ 3 , Ω be a bounded, simply connected and semiconvex domain in $${\mathbb {R}}^n$$ R n and $$L_{\Omega }:=-\Delta +V$$ L Ω : = - Δ +...

Primary 35J10 | Mathematics | Dirichlet boundary condition | Schrödinger equation | Abstract Harmonic Analysis | Musielak–Orlicz–Hardy space | Fourier Analysis | Semiconvex domain | 42B30 | Convex and Discrete Geometry | 42B20 | 46E30 | Global Analysis and Analysis on Manifolds | Secondary 42B35 | Differential Geometry | Dynamical Systems and Ergodic Theory | 42B37 | RIESZ TRANSFORMS | ORLICZ-HARDY SPACES | STRONGLY LIPSCHITZ-DOMAINS | BOUNDARY-VALUE-PROBLEMS | SMOOTH DOMAIN | SINGULAR INTEGRAL-OPERATORS | NEUMANN PROBLEMS | CONVEX DOMAINS | MATHEMATICS | R-N | Schrodinger equation | GREEN POTENTIALS | Musielak-Orlicz-Hardy space

Primary 35J10 | Mathematics | Dirichlet boundary condition | Schrödinger equation | Abstract Harmonic Analysis | Musielak–Orlicz–Hardy space | Fourier Analysis | Semiconvex domain | 42B30 | Convex and Discrete Geometry | 42B20 | 46E30 | Global Analysis and Analysis on Manifolds | Secondary 42B35 | Differential Geometry | Dynamical Systems and Ergodic Theory | 42B37 | RIESZ TRANSFORMS | ORLICZ-HARDY SPACES | STRONGLY LIPSCHITZ-DOMAINS | BOUNDARY-VALUE-PROBLEMS | SMOOTH DOMAIN | SINGULAR INTEGRAL-OPERATORS | NEUMANN PROBLEMS | CONVEX DOMAINS | MATHEMATICS | R-N | Schrodinger equation | GREEN POTENTIALS | Musielak-Orlicz-Hardy space

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2013, Volume 365, Issue 9, pp. 4729 - 4809

denote, respectively, the Dirichlet Green operator and the Neumann Green operator.]]>

Divergence form elliptic operator | Convex domain | Local orlicz-hardy space | Nontangential maximal function | Neumann boundary condition | Neumann green operator | Lusin area function | Dirichlet boundary condition | Atom | Weight | Gaussian property | Semiconvex domain | Dirichlet green operator | Strongly lipschitz domain | STRONGLY LIPSCHITZ-DOMAINS | convex domain | Dirichlet Green operator | nontangential maximal function | SMOOTH DOMAIN | HP SPACES | MATHEMATICS | GREEN POTENTIALS | divergence form elliptic operator | Neumann Green operator | local Orlicz-Hardy space | weight | DIVERGENCE OPERATORS | ELLIPTIC-OPERATORS | DIFFERENTIAL FORMS | semiconvex domain | Strongly Lipschitz domain | BOUNDARY | HEAT KERNEL | atom | 2ND-ORDER DERIVATIVES

Divergence form elliptic operator | Convex domain | Local orlicz-hardy space | Nontangential maximal function | Neumann boundary condition | Neumann green operator | Lusin area function | Dirichlet boundary condition | Atom | Weight | Gaussian property | Semiconvex domain | Dirichlet green operator | Strongly lipschitz domain | STRONGLY LIPSCHITZ-DOMAINS | convex domain | Dirichlet Green operator | nontangential maximal function | SMOOTH DOMAIN | HP SPACES | MATHEMATICS | GREEN POTENTIALS | divergence form elliptic operator | Neumann Green operator | local Orlicz-Hardy space | weight | DIVERGENCE OPERATORS | ELLIPTIC-OPERATORS | DIFFERENTIAL FORMS | semiconvex domain | Strongly Lipschitz domain | BOUNDARY | HEAT KERNEL | atom | 2ND-ORDER DERIVATIVES

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

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 03/2020, Volume 41, Issue 4, pp. 442 - 461

Let and E* denote its dual space. Let and be bounded generalized -strongly, and -strongly monotone maps, respectively. Suppose the Hammerstein equation has a...

Hammerstein equations | strongly monotone mappings | Bounded | strong convergence | NONLINEAR INTEGRAL-EQUATIONS | MATHEMATICS, APPLIED | Bounded Phi(i)-strongly monotone mappings | THEOREMS | OPERATORS | FIXED-POINTS | Iterative methods | Formulas (mathematics) | Iterative algorithms

Hammerstein equations | strongly monotone mappings | Bounded | strong convergence | NONLINEAR INTEGRAL-EQUATIONS | MATHEMATICS, APPLIED | Bounded Phi(i)-strongly monotone mappings | THEOREMS | OPERATORS | FIXED-POINTS | Iterative methods | Formulas (mathematics) | Iterative algorithms

Journal Article

Applicable Analysis: Multiscale Inverse Problems, ISSN 0003-6811, 01/2018, Volume 97, Issue 1, pp. 69 - 88

In this paper, we consider the problem of finding the function , from the final data and where is a linear, unbounded, self-adjoint and positive definite...

Regularization method | error estimate | 35K05 | 47J06 | strongly damped wave | final value problem | 35K99 | ATTRACTORS | MATHEMATICS, APPLIED | 47H10 | Operators (mathematics) | Inverse problems | Ill-posed problems (mathematics) | Regularization | Wave equations

Regularization method | error estimate | 35K05 | 47J06 | strongly damped wave | final value problem | 35K99 | ATTRACTORS | MATHEMATICS, APPLIED | 47H10 | Operators (mathematics) | Inverse problems | Ill-posed problems (mathematics) | Regularization | Wave equations

Journal Article

Afrika Matematika, ISSN 1012-9405, 12/2017, Volume 28, Issue 7, pp. 1115 - 1129

The aim of this work is to present new abstract fixed point theorems in ordered Banach spaces and on Banach algebras. The main existence results generalize...

Krasnosel’skii’s fixed point theorem | Strongly positive operator | Krein–Rutman theorem | Mathematics | History of Mathematical Sciences | 37C25 (fixed point index theory) | 47J10 (nonlinear eigenvalue problems) | Banach algebra | Cone compression and expansion | 47B48 (Banach algebra) | 45G10 (nonlinear integral equations) | Positive solution | 58C40 (spectral theory) | Mathematics, general | Mathematics Education | 47H30 (Hammerstein operator) | Integral equation | Applications of Mathematics | Homogeneous operator

Krasnosel’skii’s fixed point theorem | Strongly positive operator | Krein–Rutman theorem | Mathematics | History of Mathematical Sciences | 37C25 (fixed point index theory) | 47J10 (nonlinear eigenvalue problems) | Banach algebra | Cone compression and expansion | 47B48 (Banach algebra) | 45G10 (nonlinear integral equations) | Positive solution | 58C40 (spectral theory) | Mathematics, general | Mathematics Education | 47H30 (Hammerstein operator) | Integral equation | Applications of Mathematics | Homogeneous operator

Journal Article

ESAIM: Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 4/2009, Volume 15, Issue 2, pp. 403 - 425

In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review...

Lyapunov functionals | Hyperbolic symmetric systems | Heat exchangers | Partial differential equations | Exponential stability | Strongly continuous semigroups | MATHEMATICS, APPLIED | DECAY | STABILIZATION | exponential stability | strongly continuous semigroups | heat exchangers | WAVE-EQUATION | partial differential equations | BOUNDARY CONTROL | CONTROLLABILITY | STABILIZABILITY | AUTOMATION & CONTROL SYSTEMS

Lyapunov functionals | Hyperbolic symmetric systems | Heat exchangers | Partial differential equations | Exponential stability | Strongly continuous semigroups | MATHEMATICS, APPLIED | DECAY | STABILIZATION | exponential stability | strongly continuous semigroups | heat exchangers | WAVE-EQUATION | partial differential equations | BOUNDARY CONTROL | CONTROLLABILITY | STABILIZABILITY | AUTOMATION & CONTROL SYSTEMS

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2003, Volume 34, Issue 3, pp. 611 - 635

We consider a free boundary problem of a quasi-linear strongly degenerate parabolic equation arising from a model of pressure filtration of flocculated...

Free boundary problem | Strongly degenerate parabolic equation | Pressure filtration | Divergence-measure field | free boundary problem | strongly degenerate parabolic equation | MATHEMATICS, APPLIED | SEDIMENTATION-CONSOLIDATION PROCESSES | pressure filtration | divergence-measure field

Free boundary problem | Strongly degenerate parabolic equation | Pressure filtration | Divergence-measure field | free boundary problem | strongly degenerate parabolic equation | MATHEMATICS, APPLIED | SEDIMENTATION-CONSOLIDATION PROCESSES | pressure filtration | divergence-measure field

Journal Article

Journal of Mathematical Modelling and Algorithms in Operations Research, ISSN 2214-2487, 12/2014, Volume 13, Issue 4, pp. 405 - 423

In this paper, we introduced modified Mann iterative algorithms by the new hybrid projection method for finding a common element of the set of fixed points of...

General system of the variational inequality problem | Algorithms | Data Mining and Knowledge Discovery | Split generalized equilibrium problem | Inverse-strongly monotone mapping | Mathematics | Operations Research, Management Science | Mathematical Modeling and Industrial Mathematics | Optimization | Nonexpansive mapping | Studies | Hilbert space | Mathematical analysis | Equilibrium | Inequalities | Projection | Mathematical models | Iterative algorithms | Mapping | Convergence

General system of the variational inequality problem | Algorithms | Data Mining and Knowledge Discovery | Split generalized equilibrium problem | Inverse-strongly monotone mapping | Mathematics | Operations Research, Management Science | Mathematical Modeling and Industrial Mathematics | Optimization | Nonexpansive mapping | Studies | Hilbert space | Mathematical analysis | Equilibrium | Inequalities | Projection | Mathematical models | Iterative algorithms | Mapping | Convergence

Journal Article

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