2017, Contemporary mathematics, ISBN 9781470428365, Volume 693, vi, 411 pages

Book

1989, ISBN 0387970177, Volume 120., xvi, 308

Book

2001, Monographs in mathematics, ISBN 3764365463, Volume 97., xii, 425

Book

2013, Mathematical surveys and monographs, ISBN 0821891529, Volume 187, xxiv, 299

Book

Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2017, Volume 369, Issue 6, pp. 4063 - 4092

In this paper we study the regularity properties of fractional maximal operators acting on BV-functions...

Discrete maximal operators | Fractional maximal operator | Sobolev spaces | Bounded variation | bounded variation | MATHEMATICS | REGULARITY | discrete maximal operators | OPERATORS

Discrete maximal operators | Fractional maximal operator | Sobolev spaces | Bounded variation | bounded variation | MATHEMATICS | REGULARITY | discrete maximal operators | OPERATORS

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2014, Volume 266, Issue 7, pp. 4314 - 4421

...) is defined as the completion in the classical Sobolev space Wk,p(O) of (restrictions to O of) functions from Cc∞(Rn) whose supports are disjoint from D...

Bessel potential space and capacity | Synthesis | Locally [formula omitted]-domain | Mixed boundary value problem | Higher-order elliptic system | Ahlfors regular set | Linear extension operator | Besov and Triebel–Lizorkin spaces | Higher-order Sobolev space | Higher-order boundary trace operator | Real and complex interpolation | Locally (ε, δ)-domain | Besov and Triebel-Lizorkin spaces | DIFFERENTIABLE FUNCTIONS | Locally (epsilon, delta)-domain | STOKES SYSTEM | BESOV-SPACES | LIPSCHITZ-DOMAINS | EXTENSION-THEOREMS | INTERPOLATION | MATHEMATICS | DECOMPOSITIONS | REGULARITY | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS

Bessel potential space and capacity | Synthesis | Locally [formula omitted]-domain | Mixed boundary value problem | Higher-order elliptic system | Ahlfors regular set | Linear extension operator | Besov and Triebel–Lizorkin spaces | Higher-order Sobolev space | Higher-order boundary trace operator | Real and complex interpolation | Locally (ε, δ)-domain | Besov and Triebel-Lizorkin spaces | DIFFERENTIABLE FUNCTIONS | Locally (epsilon, delta)-domain | STOKES SYSTEM | BESOV-SPACES | LIPSCHITZ-DOMAINS | EXTENSION-THEOREMS | INTERPOLATION | MATHEMATICS | DECOMPOSITIONS | REGULARITY | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 267, Issue 4, pp. 2594 - 2615

In this paper, we show the existence and non-existence of minimizers of the following minimization problems which include an open problem mentioned by Horiuchi...

Optimal constant | Extremal function | Critical Hardy inequality | Symmetry breaking | EXISTENCE | MATHEMATICS | STATES | SYMMETRY | ELLIPTIC-EQUATIONS | SHARP CONSTANTS | SOBOLEV

Optimal constant | Extremal function | Critical Hardy inequality | Symmetry breaking | EXISTENCE | MATHEMATICS | STATES | SYMMETRY | ELLIPTIC-EQUATIONS | SHARP CONSTANTS | SOBOLEV

Journal Article

Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 11/2014, Volume 31, Issue 6, pp. 1131 - 1153

We study various boundary and inner regularity questions for p(⋅)-(super)harmonic functions in Euclidean domains...

Quasicontinuous | lsc-regularized | Sobolev space | [formula omitted]-superharmonic | Trichotomy | Semiregular point | Comparison principle | Removable singularity | Nonlinear potential theory | Variable exponent | Regular boundary point | [formula omitted]-supersolution | [formula omitted]-harmonic | Kellogg property | Nonstandard growth equation | Strongly irregular point | Obstacle problem | p(•)-superharmonic | p(•)-harmonic | p(•)-supersolution | MATHEMATICS, APPLIED | Isc-regularized | P-HARMONIC FUNCTIONS | p(.)-harmonic | p(.)-supersolution | p(.)-superharmonic | ELLIPTIC-EQUATIONS | Mathematics - Analysis of PDEs

Quasicontinuous | lsc-regularized | Sobolev space | [formula omitted]-superharmonic | Trichotomy | Semiregular point | Comparison principle | Removable singularity | Nonlinear potential theory | Variable exponent | Regular boundary point | [formula omitted]-supersolution | [formula omitted]-harmonic | Kellogg property | Nonstandard growth equation | Strongly irregular point | Obstacle problem | p(•)-superharmonic | p(•)-harmonic | p(•)-supersolution | MATHEMATICS, APPLIED | Isc-regularized | P-HARMONIC FUNCTIONS | p(.)-harmonic | p(.)-supersolution | p(.)-superharmonic | ELLIPTIC-EQUATIONS | Mathematics - Analysis of PDEs

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 266, Issue 1, pp. 44 - 69

.... We study extensions of Newtonian Sobolev functions to the completion Xˆ of X and use them to obtain several results on X itself, in particular concerning minimal weak...

Newtonian Sobolev space | Lebesgue point | Quasiminimizer | Noncomplete metric space | p-harmonic function | Poincaré inequality | QUASICONTINUITY | QUASIMINIMIZERS | LIPSCHITZ FUNCTIONS | POTENTIAL-THEORY | OPEN SETS | MATHEMATICS | QUASIOPEN | Poincare inequality | HARMONIC-FUNCTIONS

Newtonian Sobolev space | Lebesgue point | Quasiminimizer | Noncomplete metric space | p-harmonic function | Poincaré inequality | QUASICONTINUITY | QUASIMINIMIZERS | LIPSCHITZ FUNCTIONS | POTENTIAL-THEORY | OPEN SETS | MATHEMATICS | QUASIOPEN | Poincare inequality | HARMONIC-FUNCTIONS

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 1/2011, Volume 34, Issue 1, pp. 67 - 81

The Wendland radial basis functions (Wendland, Adv Comput Math 4:389–396, 1995) are piecewise polynomial compactly supported reproducing kernels in Hilbert spaces which are norm...

Numeric Computing | Theory of Computation | Positive definite functions | Kernels | Algebra | Calculus of Variations and Optimal Control; Optimization | 41A30 | 41A63 | Fractional calculus | 65D10 | Computer Science | Hypergeometric functions | Mathematics, general | Sobolev spaces | 33C90 | 41A15 | Compactly supported radial basis functions | 41A05 | 65D07 | Hypergeometric functions | Sobolev spaces | Positive definite functions | Fractional calculus | Compactly supported radial basis functions | RADIAL FUNCTIONS | MATHEMATICS, APPLIED | Functions | Calculus | Vector spaces | Research | Functional equations | Radial basis function | Computation | Sobolev space | Mathematical analysis | Hilbert space | Mathematical models

Numeric Computing | Theory of Computation | Positive definite functions | Kernels | Algebra | Calculus of Variations and Optimal Control; Optimization | 41A30 | 41A63 | Fractional calculus | 65D10 | Computer Science | Hypergeometric functions | Mathematics, general | Sobolev spaces | 33C90 | 41A15 | Compactly supported radial basis functions | 41A05 | 65D07 | Hypergeometric functions | Sobolev spaces | Positive definite functions | Fractional calculus | Compactly supported radial basis functions | RADIAL FUNCTIONS | MATHEMATICS, APPLIED | Functions | Calculus | Vector spaces | Research | Functional equations | Radial basis function | Computation | Sobolev space | Mathematical analysis | Hilbert space | Mathematical models

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 8, pp. 1461 - 1476

... versions.We prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined...

有界变差 | 分数次极大算子 | 非中心 | 离散 | 偏导数 | 点估计 | 正则性 | 分数次极大函数 | bounded variation | 42B25 | 46E35 | 26A45 | 39A12 | discrete multisublinear fractional maximal operator | discrete fractional maximal operator | continuity | Mathematics | Applications of Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | END-POINT REGULARITY | BOUNDEDNESS | OPERATORS

有界变差 | 分数次极大算子 | 非中心 | 离散 | 偏导数 | 点估计 | 正则性 | 分数次极大函数 | bounded variation | 42B25 | 46E35 | 26A45 | 39A12 | discrete multisublinear fractional maximal operator | discrete fractional maximal operator | continuity | Mathematics | Applications of Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | END-POINT REGULARITY | BOUNDEDNESS | OPERATORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2019, Volume 479, Issue 1, pp. 482 - 530

We study properties of functions with bounded variation in Carnot-Carathéodory spaces. We prove their almost everywhere approximate differentiability...

Functions with bounded variation | Carnot-Carathéodory spaces | MATHEMATICS, APPLIED | INEQUALITIES | Carnot-Caratheodory spaces | BV FUNCTIONS | VECTOR-FIELDS | SOBOLEV | MATHEMATICS | SUBMANIFOLDS | REGULARITY | THEOREMS | SETS | RECTIFIABILITY | PERIMETER

Functions with bounded variation | Carnot-Carathéodory spaces | MATHEMATICS, APPLIED | INEQUALITIES | Carnot-Caratheodory spaces | BV FUNCTIONS | VECTOR-FIELDS | SOBOLEV | MATHEMATICS | SUBMANIFOLDS | REGULARITY | THEOREMS | SETS | RECTIFIABILITY | PERIMETER

Journal Article

Advances in calculus of variations, ISSN 1864-8266, 2019, Volume 12, Issue 3, pp. 225 - 252

...] in the Hilbert case setting. In particular, after developing a rather complete theory of magnetic bounded variation functions, we prove the validity of the formula...

49A50 | Fractional magnetic spaces | BV-functions | 82D99 | Bourgain–Brezis–Mironescu formula | 26A33 | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | APPROXIMATIONS | Bourgain Brezis Mironescu formula

49A50 | Fractional magnetic spaces | BV-functions | 82D99 | Bourgain–Brezis–Mironescu formula | 26A33 | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | APPROXIMATIONS | Bourgain Brezis Mironescu formula

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 4/2019, Volume 79, Issue 1, pp. 493 - 516

In this paper a numerical simulation based on radial basis functions is presented for the time-dependent Allen...

Computational Mathematics and Numerical Analysis | Radial basis functions | Algorithms | Laplace–Beltrami operator | Time splitting scheme | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Error estimate | Mathematics | Allen–Cahn equation | SCATTERED DATA INTERPOLATION | MATHEMATICS, APPLIED | MOTION | APPROXIMATION | MODELS | Allen-Cahn equation | SPHERES | Laplace-Beltrami operator | Analysis | Numerical analysis

Computational Mathematics and Numerical Analysis | Radial basis functions | Algorithms | Laplace–Beltrami operator | Time splitting scheme | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Error estimate | Mathematics | Allen–Cahn equation | SCATTERED DATA INTERPOLATION | MATHEMATICS, APPLIED | MOTION | APPROXIMATION | MODELS | Allen-Cahn equation | SPHERES | Laplace-Beltrami operator | Analysis | Numerical analysis

Journal Article

Arkiv for Matematik, ISSN 0004-2080, 2018, Volume 56, Issue 1, pp. 147 - 161

...)<= C-n parallel to D f parallel to(1) for all radial functions in W-1,W-1(R-n).

MATHEMATICS | SOBOLEV SPACES

MATHEMATICS | SOBOLEV SPACES

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2019, Volume 132, pp. 457 - 482

Given an arbitrary planar ∞-harmonic function u, for each α>0 we establish a quantitative Wloc1,2-estimate of |Du|α...

Sobolev regularity | harmonic function | Absolute minimizer | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | infinity-harmonic function | MINIMIZATION PROBLEMS | LIPSCHITZ EXTENSIONS

Sobolev regularity | harmonic function | Absolute minimizer | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | infinity-harmonic function | MINIMIZATION PROBLEMS | LIPSCHITZ EXTENSIONS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2015, Volume 367, Issue 1, pp. 725 - 749

We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain...

Stratified vector field | Normal bundle | Approximation | Stratification | Sobolev space | Bessel process | MATHEMATICS | approximation | normal bundle | DERIVATIVES | stratified vector field

Stratified vector field | Normal bundle | Approximation | Stratification | Sobolev space | Bessel process | MATHEMATICS | approximation | normal bundle | DERIVATIVES | stratified vector field

Journal Article

St. Petersburg Mathematical Journal, ISSN 1061-0022, 06/2016, Volume 27, Issue 3, pp. 347 - 379

.... Also, similar functionals related to Musielak-Orlicz spaces are discussed, in which basic properties like the density of smooth functions, the boundedness of maximal and integral operators...

Hölder regularity of minimizers | Functionals with nonstandard growth | Holder regularity of minimizers | SMOOTH FUNCTIONS | HOLDER CONTINUITY | LOCAL REGULARITY | RELAXATION | MINIMIZERS | MATHEMATICS | INTEGRAL FUNCTIONALS | SOBOLEV SPACES | LOWER SEMICONTINUITY | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS

Hölder regularity of minimizers | Functionals with nonstandard growth | Holder regularity of minimizers | SMOOTH FUNCTIONS | HOLDER CONTINUITY | LOCAL REGULARITY | RELAXATION | MINIMIZERS | MATHEMATICS | INTEGRAL FUNCTIONALS | SOBOLEV SPACES | LOWER SEMICONTINUITY | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 06/2015, Volume 258, Issue 11, pp. 4062 - 4101

...≤α<1, an extremal function for ℓ(α) exists.

Extremal function | Trudinger–Moser inequality | Blow-up analysis | Sharp constants | Limiting Sobolev inequalities | Trudinger-Moser inequality

Extremal function | Trudinger–Moser inequality | Blow-up analysis | Sharp constants | Limiting Sobolev inequalities | Trudinger-Moser inequality

Journal Article

Mathematische annalen, ISSN 1432-1807, 2018, Volume 375, Issue 3-4, pp. 1721 - 1743

... $$W^{1,p}_0(\Omega )$$ W 0 1 , p ( Ω ) . We show that the ratio of any two extremal functions is constant provided that $$\Omega $$ Ω is convex...

39B62 | Mathematics, general | Mathematics | 35P30 | 35J60 | 35J70

39B62 | Mathematics, general | Mathematics | 35P30 | 35J60 | 35J70

Journal Article

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