Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces

2025/05/20 by Capogna, Luca, Gibara, Ryan, Korte, Riikka +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2505.14950

Abstract

We prove global Hölder regularity result for weak solutions u∈ N^1,p(Ω, μ) to a PDE of p-Laplacian type with a measure as non-homogeneous term: -div ( |∇ u|^p-2∇ u )=ν, where 1

Citations

• Fractional p-Laplacians via Neumann problems in unbounded metric measure spaces
• Higher Hölder regularity for the fractional p-Laplace equation in the subquadratic case
• Trace and extension theorems for homogeneous Sobolev and Besov spaces for unbounded uniform domains in metric measure spaces
• Solving a Dirichlet problem for unbounded domains via a conformal transformation
• Neumann problems for p-harmonic functions, and induced nonlocal operators in metric measure spaces
• Conformal transformation of uniform domains under weights that depend on distance to the boundary
• Gradient estimates for singular p-Laplace type equations with measure data
• Higher H "older regularity for the fractional p-Laplacian in the\n superquadratic case
• Trace and extension theorems for Sobolev-type functions in metric spaces
• The Poincaré inequality is an open ended condition
• Quasiconformal maps in metric spaces with controlled geometry
• On the solutions of quasi-linear elliptic partial differential equations

Cited by

• Trace and Extension Theorems for Besov Functions in Doubling Metric Measure Spaces

Related

• Fractional p-Laplacians via Neumann problems in unbounded metric measure spaces
• Hölder regularity for mixed local and nonlocal p-Laplace parabolic equations
• Hölder regularity for a class of doubly non linear PDEs
• Hölder regularity for fractional p-Laplace equations
• Hölder regularity of doubly nonlinear nonlocal quasilinear parabolic equations in some mixed singular-degenerate regime