Global Hölder regularity for the fractional p-Laplacian

2014/11/11 by Iannizzotto, Antonio, Mosconi, Sunra, Squassina, Marco · 8 citations
#35P15 #35P30 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.2956

Abstract

By virtue of barrier arguments we prove C^α-regularity up to the boundary for the weak solutions of a non-local nonlinear problem driven by the fractional p-Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular (p<2) of degenerate (p>2) case.

Cited by

• Nontrivial solutions for nonlinear problems driven by a superposition of fractional p-Laplacians with Neumann boundary conditions
• The inhomogeneous fractional Dirichlet problem
• C^1+α regularity for fractional p-harmonic functions
• On boundary regularity for the fractional p-Laplacian with unbounded reactions
• Higher Hölder regularity for fractional (p,q)-Laplace equations
• Nonlocal Harnack inequality in a disconnected region
• Hölder extension for fractional Laplacian
• Improved Hölder regularity of fractional (p,q)-Poisson equation with regular data

Related

• Fine boundary regularity for the degenerate fractional p-Laplacian
• A note on global regularity for the weak solutions of fractional\n p-Laplacian equations
• Fine boundary regularity for the singular fractional p-Laplacian
• Interior and boundary regularity results for strongly nonhomogeneous p,q-fractional problems
• A survey on boundary regularity for the fractional p-Laplacian and its applications