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documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ell^{1}$\end{document}l1-balls (1) 1
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Potential Analysis, ISSN 0926-2601, 8/2016, Volume 45, Issue 2, pp. 201 - 227
In this paper we introduce Bessel potentials and the Sobolev potential spaces resulting from them in the context of Ahlfors regular metric spaces. The Bessel... 
Geometry | Potential Theory | Functional Analysis | Bessel potential | Probability Theory and Stochastic Processes | Mathematics | 43A85 | Sobolev spaces | Besov spaces | Ahlfors spaces | Fractional derivative | MATHEMATICS | BESOV | HAJLASZ-SOBOLEV SPACES | Mathematics - Classical Analysis and ODEs
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 04/2019, Volume 168, Issue 5, pp. 775 - 848
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 6/2018, Volume 57, Issue 3, pp. 1 - 23
...Calc. Var. (2018) 57:74 https://doi.org/10.1007/s00526-018-1357-3 Calculus of Variations Quasilinear equations with natural growth in the gradients in spaces... 
Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35J92 | 35A01 | Mathematics | 35J66 | SOURCE TERMS | FRACTIONAL INTEGRALS | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | WEIGHTED INEQUALITIES | REGULARITY | POSITIVE SOLUTIONS | ELLIPTIC-EQUATIONS | DOMAINS | OPERATORS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2017, Volume 369, Issue 5, pp. 3547 - 3573
Journal Article
Journal of functional analysis, ISSN 0022-1236, 2018, Volume 275, Issue 1, pp. 1 - 44
We investigate a fractional notion of gradient and divergence operator. We generalize the div-curl estimate by Coifman–Lions–Meyer... 
Fractional div-curl lemma | Fractional harmonic maps | Fractional divergence | MATHEMATICS | THEOREM | SPACES | SURFACE | 1/2-HARMONIC MAPS | WEAKLY HARMONIC MAPS | COMPACTNESS | H-SYSTEMS | PARTIAL REGULARITY
Journal Article
Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 3/2014, Volume 15, Issue 1, pp. 133 - 153
Brezis and Mironescu have announced several years ago that for a compact manifold $${N^n \subset \mathbb{R}^\upsilon}$$ N n ⊂ R υ and for real numbers 0 < s <... 
58D15 | fractional Sobolev spaces | simply connectedness | Mathematical Methods in Physics | Sobolev maps | 46E35 | Analysis | 46T20 | Mathematics, general | Mathematics | Strong density | DENSITY | MATHEMATICS | MATHEMATICS, APPLIED | TRACE SPACES | OPERATOR | 2 MANIFOLDS | MAPPINGS | Mathematics - Functional Analysis | Analysis of PDEs
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 05/2017, Volume 154, pp. 241 - 257
In this paper we prove several formulae that enable one to capture the singular portion of the measure derivative of a function of bounded variation as a limit... 
Fractional Laplacian | Bounded variation | Non-local energies
Journal Article
Advances in Mathematics, ISSN 0001-8708, 01/2014, Volume 250, pp. 387 - 419
A weighted norm inequality of Muckenhoupt–Wheeden type is obtained for gradients of solutions to a class of quasilinear equations with measure data on Reifenberg flat domains... 
Riccati type equations | Weighted norm inequalities | Measure data | Muckenhoupt–Wheeden type inequalities | Quasilinear equations | Capacity | Muckenhoupt-Wheeden type inequalities | EXISTENCE | INEQUALITIES | TERMS | ZYGMUND THEORY | FRACTIONAL INTEGRALS | MATHEMATICS | REGULARITY | NORM | MAPPINGS | DEGENERATE ELLIPTIC-EQUATIONS
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 8, pp. 1461 - 1476
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 06/2015, Volume 47, Issue 3, pp. 396 - 406
Abstract The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalities for... 
FRACTIONAL INTEGRALS | MATHEMATICS | MAXIMAL FUNCTIONS | HORMANDER VECTOR-FIELDS | METRICS | POINCARE INEQUALITIES | REPRESENTATION FORMULAS | OPERATORS
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2006, Volume 194, Issue 1, pp. 94 - 114
Journal Article
Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 18
Journal Article
Communications in partial differential equations, ISSN 0360-5302, 12/2009, Volume 34, Issue 12, pp. 1607 - 1631
Γ-convergence methods are used to prove homogenization results for fractional obstacle problems in periodically perforated domains. The obstacles have random... 
Fractional obstacles | Perforated domains | Γ-Convergence | Weighted Sobolev energies
Journal Article
Potential Analysis, ISSN 0926-2601, 3/2017, Volume 46, Issue 3, pp. 403 - 430
We study nonlinear elliptic equations in divergence form div A ( x , Du ) = div G . $\text {div }{\mathcal A}(x,Du)=\text {div } G.$ When A ${\mathcal A}$ has... 
35J60 | Probability Theory and Stochastic Processes | Mathematics | Nonlinear elliptic equations | Besov spaces | Geometry | Potential Theory | Functional Analysis | Higher order fractional differentiability | 49N60 | Local well-posedness | 35B65 | 42B37 | MATHEMATICS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 08/2020, Volume 293, Issue 8, pp. 1459 - 1480
We establish the higher fractional differentiability of the solutions of a problem in divergence form of the type divA(x,Du)=div|F|p(x)−22FinΩ,u=0on∂Ω.The main... 
variable exponents | nonlinear elliptic equations | p(x)‐Laplacian operator | Besov spaces | higher order fractional differentiability
Journal Article
Journal of Inequalities and Applications, 12/2018, Volume 2018, Issue 1, pp. 1 - 17
In this paper we investigate the endpoint regularity of the discrete m-sublinear fractional maximal operator associated with ℓ1 $\ell^{1}$-balls, both in the... 
26A45 | Sobolev space | Mathematics | Discrete multisublinear fractional maximal function | ℓ 1 $\ell^{1}$ -balls | 42B25 | 46E35 | 39A12 | Bounded variation | Analysis | Mathematics, general | Continuity | Applications of Mathematics
Journal Article
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