Boundedness of Wolff-type potentials and applications to PDEs
Analysis of PDEs
2023-10-13 v2
Abstract
We provide a short proof of a sharp rearrangement estimate for a generalized version of a potential of Wolff--Havin--Maz'ya type. As a consequence, we prove a reduction principle for that integral operators, that is, a characterization of those rearrangement invariant spaces between which the potentials are bounded via a one-dimensional inequality of Hardy-type. Since the special case of the mentioned potential is known to control precisely very weak solutions to a broad class of quasilinear elliptic PDEs of non-standard growth, we infer the local regularity properties of the solutions in rearrangement invariant spaces for prescribed classes of data.
Keywords
Cite
@article{arxiv.2209.05618,
title = {Boundedness of Wolff-type potentials and applications to PDEs},
author = {Michał Borowski and Iwona Chlebicka and Błażej Miasojedow},
journal= {arXiv preprint arXiv:2209.05618},
year = {2023}
}