Fractional capacities relative to bounded open Lipschitz sets complemented

DOI10.1007/s00526-016-1105-5zbMath1362.31002OpenAlexW2566349946MaRDI QIDQ522250

Shaoguang Shi, Jie Xiao

Publication date: 13 April 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-016-1105-5

zbMATH Keywords

fractional Sobolev spacefractional capacitiesfractional Lapace equation

Mathematics Subject Classification ID

Connections of harmonic functions with differential equations in higher dimensions (31B35) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items

A capacity associated with the weighted Lebesgue space and its applications, Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian, Rough singular integrals associated to polynomial curves, Fractional non-linear regularity, potential and balayage, Regularity of commutator of bilinear maximal operator with Lipschitz symbols, Characterization of fractional Sobolev-Poincaré and (localized) Hardy inequalities, Dual characterization of fractional capacity via solution of fractional p‐Laplace equation, Besov capacity for a class of nonlocal hypoelliptic operators and its applications, Characterizations of the viscosity solution of a nonlocal and nonlinear equation induced by the fractional \(p\)-Laplace and the fractional \(p\)-convexity, The logarithmic Sobolev capacity, Some notes on supersolutions of fractional \(p\)-Laplace equation, Some integrability estimates for solutions of the fractional p-Laplace equation, Differentiability of logarithmic Besov functions in terms of capacities, Regularity of local multilinear fractional maximal and strong maximal operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On fractional capacities relative to bounded open Lipschitz sets
• On fractional Poincaré inequalities
• Hitchhiker's guide to the fractional Sobolev spaces
• Optimal geometric estimates for fractional Sobolev capacities
• Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation
• Strong \(A_{\infty}\)-weights and scaling invariant Besov capacities
• Measure density and extendability of Sobolev functions
• Capacity methods in the theory of partial differential equations
• The capacity of slender toroidal sets in \({\mathbb{R}{}}^ N\)
• Choquet integrals in potential theory
• Strong type estimates for homogeneous Besov capacities
• The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets
• A Hölder infinity Laplacian
• A lower bound for electrostatic capacity in the plane
• Strong type estimate and Carleson measures for Lipschitz spaces
• Some results on functional capacity and their applications to P-Laplacian problems involving measure data
• Anisotropic Sobolev Capacity with Fractional Order
• Capacities and embeddings via symmetrization and conductor inequalities
• Fractional Sobolev extension and imbedding