Duke mathematical journal, ISSN 00127094, 04/2011, Volume 157, Issue 2, pp. 421  423
Journal Article
Duke mathematical journal, ISSN 00127094, 05/2010, Volume 153, Issue 1, pp. 1  22
Journal Article
Hiroshima mathematical journal, ISSN 00182079, 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
31B15
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 09442669, 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
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 00217824, 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  ELLIPTICEQUATIONS  POTENTIALS  SCHRODINGEROPERATORS
Green's function  Strong maximum principle  Schrödinger operator  Singular potential  EXISTENCE  MATHEMATICS  MATHEMATICS, APPLIED  KATOS INEQUALITY  Schrodinger operator  ELLIPTICEQUATIONS  POTENTIALS  SCHRODINGEROPERATORS
Journal Article
Communications in Contemporary Mathematics, ISSN 02191997, 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  gfunction
average  Lusin area function  g function  Riesz potential operator  Sobolev space  function  MATHEMATICS  MATHEMATICS, APPLIED  AVERAGES  g(lambda)function  gfunction
Journal Article
Potential Analysis, ISSN 09262601, 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  POTENTIALTHEORY  PRINCIPLE  MATHEMATICS  RANDOMWALKS  Levy process  GROWTH  METRIC MEASURESPACES  JUMPPROCESSES
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  POTENTIALTHEORY  PRINCIPLE  MATHEMATICS  RANDOMWALKS  Levy process  GROWTH  METRIC MEASURESPACES  JUMPPROCESSES
Journal Article
Advances in Nonlinear Analysis, ISSN 21919496, 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  NAVIERSTOKES EQUATIONS  VARIABLES  HPSPACES
Trace  associate Morrey potential  42B35  46E35  embedding  31B15  MATHEMATICS  MATHEMATICS, APPLIED  NAVIERSTOKES EQUATIONS  VARIABLES  HPSPACES
Journal Article
Advances in Nonlinear Analysis, ISSN 21919496, 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
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 14320835, 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}$$
R
N
, establishing a symmetry...
Systems Theory, Control  Calculus of Variations and Optimal Control; Optimization  Analysis  Theoretical, Mathematical and Computational Physics  35A23  35B65  Mathematics  35J25  31B15  MATHEMATICS  MATHEMATICS, APPLIED  PARTIALDIFFERENTIALEQUATIONS  GRADIENT BOUNDS  HYPERSURFACES  INEQUALITY  DEGENERATE  DOMAINS  WULFF SHAPE  Anisotropy
Systems Theory, Control  Calculus of Variations and Optimal Control; Optimization  Analysis  Theoretical, Mathematical and Computational Physics  35A23  35B65  Mathematics  35J25  31B15  MATHEMATICS  MATHEMATICS, APPLIED  PARTIALDIFFERENTIALEQUATIONS  GRADIENT BOUNDS  HYPERSURFACES  INEQUALITY  DEGENERATE  DOMAINS  WULFF SHAPE  Anisotropy
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 09442669, 2/2018, Volume 57, Issue 1, pp. 1  31
In this paper, combining the pcapacity for $$p\in (1, n)$$
p∈(1,n)
with the Orlicz addition of convex domains, we develop the pcapacitary...
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
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 01764276, 2/2018, Volume 47, Issue 1, pp. 119  140
We prove a large deviation principle for the sequence of pushforwards 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
Large deviation principle  60F10  Numerical Analysis  Analysis  Mathematics  31B15  Riesz potential  MATHEMATICS
Journal Article
Manuscripta Mathematica, ISSN 00252611, 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
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 18648258, 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 BVspace.
28C20  Gaussian perimeter  58C35  60B11  Gaussian ℬ𝒱 capacity  31B15  Gaussian volume
28C20  Gaussian perimeter  58C35  60B11  Gaussian ℬ𝒱 capacity  31B15  Gaussian volume
Journal Article
Analysis & PDE, ISSN 21575045, 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  GREENSFUNCTIONS  SPACES  EQUATIONS  POTENTIALS  weighted norm inequalities  sublinear elliptic equations  weak maximum principle  MATHEMATICS  fractional Laplacian  OPERATORS
Weighted norm inequalities  Green's function  Fractional Laplacian  Sublinear elliptic equations  Weak maximum principle  MATHEMATICS, APPLIED  INEQUALITIES  GREENSFUNCTIONS  SPACES  EQUATIONS  POTENTIALS  weighted norm inequalities  sublinear elliptic equations  weak maximum principle  MATHEMATICS  fractional Laplacian  OPERATORS
Journal Article
16.
Full Text
Sharp capacity estimates for annuli in weighted $$\mathbf {R}^n$$ R n and in metric spaces
Mathematische Zeitschrift, ISSN 00255874, 8/2017, Volume 286, Issue 3, pp. 1173  1215
We obtain estimates for the nonlinear variational capacity of annuli in weighted
$$\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
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 09262601, 1/2018, Volume 48, Issue 1, pp. 49  84
We consider the minimum energy problem on the unit sphere
S
d

1
$\mathbb {S}^{d1}$
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
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 20384815, 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  LP SPACES
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  LP SPACES
Journal Article
Constructive Approximation, ISSN 01764276, 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
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 00114642, 3/2019, Volume 69, Issue 1, pp. 207  223
We are concerned with the boundedness of generalized fractional integral operators I
ϱ,τ
from Orlicz spaces L
Φ(X) near L
1(X) to Orlicz spaces L
Ψ(X) over...
metric measure space  Mathematics  fractional integral  31B15  Ordinary Differential Equations  46E35  Analysis  Convex and Discrete Geometry  46E30  Mathematics, general  Orlicz space  Mathematical Modeling and Industrial Mathematics  lower Ahlfors regular  Riesz potential  MATHEMATICS  SOBOLEV EMBEDDINGS  INEQUALITIES  CALDERONZYGMUND OPERATORS  MORREY SPACES  RIESZPOTENTIALS
metric measure space  Mathematics  fractional integral  31B15  Ordinary Differential Equations  46E35  Analysis  Convex and Discrete Geometry  46E30  Mathematics, general  Orlicz space  Mathematical Modeling and Industrial Mathematics  lower Ahlfors regular  Riesz potential  MATHEMATICS  SOBOLEV EMBEDDINGS  INEQUALITIES  CALDERONZYGMUND OPERATORS  MORREY SPACES  RIESZPOTENTIALS
Journal Article
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