Nonlinear gradient estimates for elliptic double obstacle problems with measure data

TL;DR

This paper establishes gradient estimates for complex elliptic double obstacle problems with measure data, advancing understanding of regularity in nonlinear PDEs with variable growth conditions.

Contribution

It provides a global Calderón-Zygmund estimate for solutions to nonlinear elliptic double obstacle problems with measure data, a novel regularity result in this context.

Findings

Gradient estimates depend on the obstacles and measure data.

Minimal regularity conditions are identified for the estimates.

Results extend regularity theory to variable exponent growth problems.

Abstract

We study quasilinear elliptic double obstacle problems with a variable exponent growth when the right-hand side is a measure. A global Calder\'{o}n-Zygmund estimate for the gradient of an approximable solution is obtained in terms of the associated double obstacles and a given measure, identifying minimal requirements for the regularity estimate.