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arXiv · 2209.05618

Boundedness of Wolff-type potentials and applications to PDEs

Michał Borowski·Iwona Chlebicka·Błażej Miasojedow
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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.

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Michał Borowski, Iwona Chlebicka, Błażej Miasojedow. 2022-09-12. Boundedness of Wolff-type potentials and applications to PDEs. https://arxiv.org/abs/2209.05618

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