Dual characterization of fractional capacity via solution of fractional p‐Laplace equation

DOI10.1002/mana.201800438zbMath1527.35153OpenAlexW3082153731MaRDI QIDQ6057374

Lei Zhang, Shaoguang Shi

Publication date: 4 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201800438

zbMATH Keywords

measure datafractional \(p\)-Laplacian

Mathematics Subject Classification ID

Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92)

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Cites Work

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• Existence results for fractional \(p\)-Laplacian problems via Morse theory
• On fractional capacities relative to bounded open Lipschitz sets
• Local behavior of fractional \(p\)-minimizers
• Higher Sobolev regularity for the fractional \(p\)-Laplace equation in the superquadratic case
• Hitchhiker's guide to the fractional Sobolev spaces
• Fractional Sobolev, Moser-Trudinger, Morrey-Sobolev inequalities under Lorentz norms
• Fractional capacities relative to bounded open Lipschitz sets complemented
• Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation
• Strong type estimates for homogeneous Besov capacities
• The Dirichlet problem for the \(p\)-fractional Laplace equation
• Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations
• Some notes on supersolutions of fractional \(p\)-Laplace equation
• The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets
• Equivalence of solutions to fractional \(p\)-Laplace type equations
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• The obstacle problem for nonlinear integro-differential operators
• Fractional eigenvalues
• Regularity of solutions to the parabolic fractional obstacle problem
• Regularity Issues Involving the Fractional p-Laplacian
• Anisotropic Sobolev Capacity with Fractional Order
• FRACTIONAL SOBOLEV–POINCARÉ AND FRACTIONAL HARDY INEQUALITIES IN UNBOUNDED JOHN DOMAINS
• Fractional p-eigenvalues
• Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions