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