Convex Symmetrization for Anisotropic Elliptic Equations with a lower order term

TL;DR

This paper develops sharp estimates for solutions to anisotropic elliptic equations with lower order terms using convex symmetrization, generalized total variation, and isoperimetric inequalities, enhancing understanding of solution behavior.

Contribution

It introduces a generalized convex symmetrization approach to derive sharp bounds for solutions and their gradients in anisotropic elliptic equations with lower order terms.

Findings

Sharp estimates for solutions and gradients obtained

Comparison with convex symmetrized solutions established

Method enhances analysis of anisotropic elliptic equations

Abstract

We use "generalized" version of total variation, coarea formulas, isoperimetric inequalities to obtain sharp estimates for solutions (and for their gradients) to anisotropic elliptic equations with a lower order term, comparing them with the solutions to the convex symmetrized ones.