
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.
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