Singular multiple integrals and nonlinear potentials

TL;DR

This paper establishes precise regularity criteria for complex nonlinear integrals with nonhomogeneous growth, advancing the understanding of potential theory in mathematical analysis.

Contribution

It introduces new sharp partial regularity criteria for nonlinear potential theoretic integrals with $(p,q)$-growth conditions.

Findings

Sharp partial regularity criteria derived

Extension of potential theory to nonhomogeneous integrals

Improved understanding of singular multiple integrals

Abstract

We prove sharp partial regularity criteria of nonlinear potential theoretic nature for the Lebesgue-Serrin-Marcellini extension of nonhomogeneous singular multiple integrals featuring $(p,q)$-growth conditions.