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Duke mathematical journal, ISSN 0012-7094, 04/2011, Volume 157, Issue 2, pp. 421 - 423
In our previous paper we studied some questions related to the {\mathcal C}^1 and Lipschitz harmonic capacities. A serious error was found in the arguments. In... 
31B05 | 31B15
Journal Article
Duke mathematical journal, ISSN 0012-7094, 05/2010, Volume 153, Issue 1, pp. 1 - 22
The Lipschitz and {\mathcal C}^{1} harmonic capacities \kappa and \kappa_{c} in {\mathbb R}^{n} can be considered as high-dimensional versions of the so-called... 
31B05 | 31B15
Journal Article
Hiroshima mathematical journal, ISSN 0018-2079, 03/2003, Volume 33, Issue 1, pp. 43 - 57
The aim in the present paper is to give a weighted version of Koskela [Ark. Mat. 37 (1999), 291–304] concerning removable sets for Sobolev functions. 
31B15
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 2/2019, Volume 58, Issue 1, pp. 1 - 21
We give necessary and sufficient conditions for the existence of a positive solution with zero boundary values to the elliptic equation $$\begin{aligned}... 
Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Secondary 31B10 | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Primary 35J61 | 42B37 | 31B15 | MATHEMATICS | MATHEMATICS, APPLIED | Energy industry | Mathematics - Analysis of PDEs
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 02/2020, Volume 134, pp. 72 - 121
Given any Borel function V:Ω→[0,+∞] on a smooth bounded domain Ω⊂RN, we establish that the strong maximum principle for the Schrödinger operator −Δ+V in Ω... 
Green's function | Strong maximum principle | Schrödinger operator | Singular potential | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | KATOS INEQUALITY | Schrodinger operator | ELLIPTIC-EQUATIONS | POTENTIALS | SCHRODINGER-OPERATORS
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 11/2018, Volume 20, Issue 7, p. 1750077
In this paper, the authors characterize the Sobolev spaces W α , p ( ℝ n ) with α ∈ ( 0 , 2 ] and p ∈ ( max { 1 , 2 n 2 α + n } , ∞ ) via a generalized Lusin... 
average | Lusin area function | g -function | Riesz potential operator | Sobolev space | function | MATHEMATICS | MATHEMATICS, APPLIED | AVERAGES | g(lambda)-function | g-function
Journal Article
Potential Analysis, ISSN 0926-2601, 7/2014, Volume 41, Issue 1, pp. 1 - 29
We prove the scale invariant Harnack inequality and regularity properties for harmonic functions with respect to an isotropic unimodal Lévy process with the... 
Lévy process | 60G51 | Probability Theory and Stochastic Processes | Mathematics | Green function | 31B15 | Harmonic function | Geometry | Harnack inequality | Subordinate Brownian motion | Potential Theory | Functional Analysis | Capacity | Potential measure | 60J45 | POTENTIAL-THEORY | PRINCIPLE | MATHEMATICS | RANDOM-WALKS | Levy process | GROWTH | METRIC MEASURE-SPACES | JUMP-PROCESSES
Journal Article
Advances in Nonlinear Analysis, ISSN 2191-9496, 08/2018, Volume 7, Issue 3, pp. 407 - 424
As a solution to the restriction question for associate Morrey potentials (Question ), this paper characterizes a Radon measure μ on such that the Riesz... 
Trace | associate Morrey potential | 42B35 | 46E35 | embedding | 31B15 | MATHEMATICS | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | VARIABLES | HP-SPACES
Journal Article
Advances in Nonlinear Analysis, ISSN 2191-9496, 08/2017, Volume 6, Issue 3, pp. 317 - 326
This paper offers a new perspective to look at the Riesz potential. On the one hand, it is shown that not only contains under the conditions , , , , but also... 
Morrey and Campanato spaces | Radon measure | 31B15 | 46E30 | Riesz potential | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | HP SPACES | MORREY SPACES
Journal Article
Calculus of variations and partial differential equations, ISSN 1432-0835, 2016, Volume 55, Issue 4, pp. 1 - 24
We consider an overdetermined problem for the Finsler Laplacian in the exterior of a convex domain in $${\mathbb {R}}^{N}$$ R N , establishing a symmetry... 
Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35A23 | 35B65 | Mathematics | 35J25 | 31B15 | MATHEMATICS | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | GRADIENT BOUNDS | HYPERSURFACES | INEQUALITY | DEGENERATE | DOMAINS | WULFF SHAPE | Anisotropy
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 2/2018, Volume 57, Issue 1, pp. 1 - 31
In this paper, combining the p-capacity for $$p\in (1, n)$$ p∈(1,n) with the Orlicz addition of convex domains, we develop the p-capacitary... 
52A20 | 52B45 | 53A15 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35J60 | Analysis | Theoretical, Mathematical and Computational Physics | 52A39 | Mathematics | 31B15 | MATHEMATICS | MATHEMATICS, APPLIED | AFFINE | INEQUALITIES | LIPSCHITZ
Journal Article
Constructive Approximation, ISSN 0176-4276, 2/2018, Volume 47, Issue 1, pp. 119 - 140
We prove a large deviation principle for the sequence of push-forwards of empirical measures in the setting of Riesz potential interactions on compact subsets... 
Large deviation principle | 60F10 | Numerical Analysis | Analysis | Mathematics | 31B15 | Riesz potential | MATHEMATICS
Journal Article
Manuscripta Mathematica, ISSN 0025-2611, 1/2016, Volume 149, Issue 1, pp. 45 - 62
In this note, we obtain sharp bounds for the Green’s function of the linearized Monge–Ampère operators associated to convex functions with either Hessian... 
Geometry | 35J75 | 35J96 | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 35J70 | 35J08 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 31B15 | MATHEMATICS | EQUATION
Journal Article
Advances in Calculus of Variations, ISSN 1864-8258, 04/2016, Volume 9, Issue 2, pp. 187 - 200
In this paper, Gaussian ℬ𝒱 capacity is introduced, developed, and subsequently applied to the trace theory of Gaussian BV-space. 
28C20 | Gaussian perimeter | 58C35 | 60B11 | Gaussian ℬ𝒱 capacity | 31B15 | Gaussian volume
Journal Article
Analysis & PDE, ISSN 2157-5045, 2018, Volume 11, Issue 2, pp. 439 - 466
We study the weighted norm inequality of (1, q )-type, parallel to G nu parallel to(q)(L)(Omega, d sigma) <= C parallel to nu parallel to for all nu is an... 
Weighted norm inequalities | Green's function | Fractional Laplacian | Sublinear elliptic equations | Weak maximum principle | MATHEMATICS, APPLIED | INEQUALITIES | GREENS-FUNCTIONS | SPACES | EQUATIONS | POTENTIALS | weighted norm inequalities | sublinear elliptic equations | weak maximum principle | MATHEMATICS | fractional Laplacian | OPERATORS
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2017, Volume 286, Issue 3, pp. 1173 - 1215
We obtain estimates for the nonlinear variational capacity of annuli in weighted $$\mathbf {R}^n$$ R n and in metric spaces. We introduce four different... 
Metric space | Sobolev space | Newtonian space | Secondary 30C65 | 31E05 | Mathematics | 30L99 | p$$ p -admissible weight | 31C15 | 31B15 | Poincaré inequality | Primary 31C45 | Exponent sets | Variational capacity | Mathematics, general | Annulus | Radial weight | Quasiconformal mapping | Doubling measure
Journal Article
Potential Analysis, ISSN 0926-2601, 1/2018, Volume 48, Issue 1, pp. 49 - 84
We consider the minimum energy problem on the unit sphere S d - 1 $\mathbb {S}^{d-1}$ in the Euclidean space R d $\mathbb {R}^{d}$ , d = 3, in the presence of... 
Minimum energy problem | 31B10 | Probability Theory and Stochastic Processes | Mathematics | 31B05 | 31B15 | Geometry | Potential Theory | Functional Analysis | Equilibrium measure | Newtonian potential | Weighted energy | Extremal measure | MATHEMATICS | EXTERNAL FIELDS | SPHERE | SEPARATION | POINTS
Journal Article
Collectanea mathematica (Barcelona), ISSN 2038-4815, 2017, Volume 69, Issue 3, pp. 377 - 394
Our aim in this paper is to establish variable exponent weighted norm inequalities for generalized Riesz potentials on the unit ball via norm inequalities in... 
Geometry | Sobolev integral representation | Weighted norm inequality | Algebra | Primary 46E30 | Analysis | Riesz potentials | Mathematics | Applications of Mathematics | Sobolev’s inequality | 31B15 | Variable exponent | MATHEMATICS | MATHEMATICS, APPLIED | Sobolev's inequality | L-P SPACES
Journal Article
Constructive Approximation, ISSN 0176-4276, 2/2018, Volume 47, Issue 1, pp. 75 - 88
We compute the expected Riesz energy of random points on flat tori drawn from certain translation invariant determinantal processes and determine the process... 
Epstein zeta function | Rearrangement inequality | Numerical Analysis | Analysis | Torus | Determinantal processes | Mathematics | Riesz energy | 31B15 | 11E45 | MATHEMATICS | MINIMA | Teoria de nombres | Potential theory (Mathematics) | Grups algebraics lineals | Teoria del potencial (Matemàtica) | Linear algebraic groups | Number theory
Journal Article
Czechoslovak Mathematical Journal, ISSN 0011-4642, 3/2019, Volume 69, Issue 1, pp. 207 - 223
Journal Article
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