The Nonlocal Almgren Problem

Emanuel Indrei ()
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Emanuel Indrei: Department of Mathematics, Kennesaw State University, Marietta, GA 30060, USA

Mathematics, 2025, vol. 13, issue 17, 1-20

Abstract: In the nonlocal Almgren problem, the goal is to investigate the convexity of a minimizer under a mass constraint via a nonlocal free energy generated with a nonlocal perimeter and convex potential. In this paper, the main result is a quantitative stability theorem for the nonlocal free energy under a symmetry assumption on the potential. In addition, several results that involve uniqueness, non-existence, and moduli estimates from the theory of crystals are also proven in the nonlocal context.

Keywords: nonlocal Almgren problem; nonlocal perimeter; nonlocal free energy; convex potential; quantitative stability; mass constraint; crystals; moduli bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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