Optimal constant for the trace inequality in $BV$ for domains with corners

TL;DR

This paper finds the exact optimal constant in the trace inequality for BV functions on domains with corners, addressing a specific class of singularities.

Contribution

It provides an explicit value for the optimal trace inequality constant in BV spaces for domains with corner singularities.

Findings

Explicit optimal constant determined for domains with corners.

Addresses trace inequalities in BV spaces with singular boundary points.

Enhances understanding of boundary behavior in BV functions.

Abstract

We determine the explicit value of the optimal constant in the trace inequality for functions of bounded variations in the case the domain has a particular class of singularities.