Boundedness of Wolff-type potentials and applications to PDEs
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS(2024)
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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Key words
Potential estimates,Quasilinear elliptic PDEs,Rearrangement,Regularity,Wolff potential
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