Nonlinear nonlocal potential theory at the gradient level

L Diening, K Kim, HS Lee, S Nowak - arXiv preprint arXiv:2402.04809, 2024 - arxiv.org
The aim of this work is to establish numerous interrelated gradient estimates in the nonlinear
nonlocal setting. First of all, we prove that weak solutions to a class of homogeneous …

Perron solutions and boundary regularity for nonlocal nonlinear Dirichlet problems

A Björn, J Björn, M Kim - arXiv preprint arXiv:2406.05994, 2024 - arxiv.org
For nonlinear operators of fractional $ p $-Laplace type, we consider two types of solutions
to the nonlocal Dirichlet problem: Sobolev solutions based on fractional Sobolev spaces and …