On nonlocal minimal graphs

TL;DR

This paper develops a functional analytic framework to study nonlocal minimal graphs, establishing fundamental theoretical results such as existence, uniqueness, and various inequalities, advancing understanding of nonlocal variational problems.

Contribution

It introduces a comprehensive functional analytic approach to nonlocal minimal graphs, proving key properties and equivalences that were previously not well-understood.

Findings

Existence and uniqueness of solutions established

A priori estimates and comparison principles derived

Equivalence of different notions of minimizers shown

Abstract

We develop a functional analytic approach for the study of nonlocal minimal graphs. Through this, we establish existence and uniqueness results, a priori estimates, comparison principles, rearrangement inequalities, and the equivalence of several notions of minimizers and solutions.