Functional Inequalities on Simple Edge Spaces

TL;DR

This paper investigates whether classical functional inequalities like Sobolev and Poincaré hold on compact simple edge spaces, and establishes an optimality result for the Sobolev inequality's B-constant.

Contribution

It extends the understanding of functional inequalities to simple edge spaces and provides an optimality result for the Sobolev inequality's B-constant.

Findings

Sobolev and Poincaré inequalities hold on compact simple edge spaces

An optimality result for the B-constant of the Sobolev inequality is obtained

The methods adapt classical inequalities to the edge space setting

Abstract

In this paper we are focusing on functional inequalities on compact simple edge spaces. More precisely we address the question whether the classical functional inequalities (Sobolev, Poincar\'e) hold in this setting, and as a by-product of our methods we obtain an optimality result concerning the $B-$constant of the Sobolev inequality.