Nonlocal equations with degenerate weights
Analysis of PDEs
2024-09-19 v1
Abstract
We introduce fractional weighted Sobolev spaces with degenerate weights. For these spaces we provide embeddings and Poincar\'e inequalities. When the order of fractional differentiability goes to or , we recover the weighted Lebesgue and Sobolev spaces with Muckenhoupt weights, respectively. Moreover, we prove interior H\"older continuity and Harnack inequalities for solutions to the corresponding weighted nonlocal integro-differential equations. This naturally extends a classical result by Fabes, Kenig, and Serapioni to the nonlinear, nonlocal setting.
Cite
@article{arxiv.2409.11829,
title = {Nonlocal equations with degenerate weights},
author = {Linus Behn and Lars Diening and Jihoon Ok and Julian Rolfes},
journal= {arXiv preprint arXiv:2409.11829},
year = {2024}
}