A borderline case of Calder\'on-Zygmund estimates for non-uniformly elliptic problems

TL;DR

This paper establishes nonlinear Calderón-Zygmund estimates for a class of non-uniformly elliptic problems with double phase energies, addressing a previously unhandled borderline case.

Contribution

It extends Calderón-Zygmund theory to non-uniformly elliptic problems in a borderline setting involving double phase energies.

Findings

Valid nonlinear Calderón-Zygmund estimates are proven for the specified class.

The results fill a gap in the theory for borderline non-uniform ellipticity.

The work broadens the applicability of regularity results in elliptic PDEs.

Abstract

We show, in a borderline case which was not covered before, the validity of nonlinear Calder\'on-Zygmund estimates for a class of non-uniformly elliptic problems driven by double phase energies.