Self Improving Sobolev-Poincare Inequalities, Truncation and Symmetrization

TL;DR

This paper extends a method for Sobolev symmetrization inequalities to functions that do not vanish at the boundary, broadening the applicability of previous results in Sobolev space analysis.

Contribution

It introduces an extension of the symmetrization inequality method to non-vanishing boundary functions in Sobolev spaces.

Findings

Extended symmetrization inequalities to boundary-non-vanishing functions

Developed new truncation techniques for Sobolev functions

Provided theoretical framework for boundary behavior in Sobolev inequalities

Abstract

In a previous paper we developed a new method to obtain symmetrization inequalities of Sobolev type for functions in $W_{0}^{1,1}(\Omega)$. In this paper we extend our method to Sobolev functions that do not vanish at the boundary.