On fractional capacities relative to bounded open Lipschitz sets

DOI10.1007/s11118-016-9545-2zbMath1348.31001OpenAlexW2290364266MaRDI QIDQ309000

Shaoguang Shi, Jie Xiao

Publication date: 6 September 2016

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-016-9545-2

zbMATH Keywords

fractional Sobolev spacefractional capacityfractional Laplace 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 (21)

Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian ⋮ Fractional non-linear regularity, potential and balayage ⋮ Existence of positive solutions for third-order semipositone boundary value problems on time scales ⋮ Optimal partition problems for the fractional Laplacian ⋮ 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 ⋮ BV capacity and perimeter in abstract Wiener spaces and applications ⋮ Regularity of commutators of the bilinear maximal operator ⋮ Some results of capacity in fractional Sobolev spaces with variable exponents ⋮ An optimal lower bound in fractional spectral geometry for planar sets with topological constraints ⋮ On simple eigenvalues of the fractional Laplacian under removal of small fractional capacity sets ⋮ Unnamed Item ⋮ The logarithmic Sobolev capacity ⋮ Some notes on supersolutions of fractional \(p\)-Laplace equation ⋮ Fractional capacities relative to bounded open Lipschitz sets complemented ⋮ Some integrability estimates for solutions of the fractional p-Laplace equation ⋮ Unnamed Item ⋮ A class of shape optimization problems for some nonlocal operators ⋮ A fractional Laplacian problem with mixed singular nonlinearities and nonregular data ⋮ Differentiability of logarithmic Besov functions in terms of capacities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hitchhiker's guide to the fractional Sobolev spaces
• The fractional Cheeger problem
• Fractional Sobolev, Moser-Trudinger, Morrey-Sobolev inequalities under Lorentz norms
• Optimal geometric estimates for fractional Sobolev capacities
• A quantitative isoperimetric inequality for fractional perimeters
• Proprietà di alcune classi di funzioni in più variabili
• Weighted inequalities and degenerate elliptic partial differential equations
• Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation
• Strong \(A_{\infty}\)-weights and scaling invariant Besov capacities
• Function spaces and wavelets on domains
• Dirichlet forms and analysis on Wiener space
• Strong type estimates for homogeneous Besov capacities
• Relative \(\infty\)-capacity and its affinization
• The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets
• Fractional eigenvalues
• Theory of capacities
• A Hölder infinity Laplacian
• Strong type estimate and Carleson measures for Lipschitz spaces
• Characterizations to the fractional Sobolev inequality
• Anisotropic Sobolev Capacity with Fractional Order
• FRACTIONAL SOBOLEV–POINCARÉ AND FRACTIONAL HARDY INEQUALITIES IN UNBOUNDED JOHN DOMAINS
• Capacities and embeddings via symmetrization and conductor inequalities
• An Extension Problem Related to the Fractional Laplacian
• Fractional Sobolev extension and imbedding

This page was built for publication: On fractional capacities relative to bounded open Lipschitz sets