$L^\infty$-variational problems associated to measurable Finsler structures

TL;DR

This paper investigates $L^ Infty$-variational problems linked to measurable Finsler structures in Euclidean spaces, establishing fundamental existence and uniqueness results for absolute minimizers.

Contribution

It provides the first rigorous analysis of $L^ Infty$-variational problems in the context of measurable Finsler structures, including existence and uniqueness theorems.

Findings

Existence of absolute minimizers established.

Uniqueness of solutions proven.

Framework for $L^ Infty$-problems in Finsler geometry developed.

Abstract

We study $L^\infty$-variational problems associated to measurable Finsler structures in Euclidean spaces. We obtain existence and uniqueness results for the absolute minimizers.