The Talenti comparison result in a quantitative form

TL;DR

This paper provides a quantitative version of Talenti's classical comparison result for elliptic problems, utilizing enhanced inequalities to measure the differences explicitly.

Contribution

It introduces a quantitative form of Talenti's comparison theorem, advancing the understanding of elliptic problem solutions through precise inequality estimates.

Findings

Quantitative bounds for elliptic problem solutions

Enhanced Pólya-Szegő and Hardy-Littlewood inequalities

Explicit comparison metrics for elliptic PDEs

Abstract

In this paper, we obtain a quantitative version of the classical comparison result of Talenti for elliptic problems with Dirichlet boundary conditions. The key role is played by quantitative versions of the P\'olya-Szego inequality and of the Hardy-Littlewood inequality.