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The Nonlocal Almgren Problem

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  • Emanuel Indrei

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

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.

Suggested Citation

  • Emanuel Indrei, 2025. "The Nonlocal Almgren Problem," Mathematics, MDPI, vol. 13(17), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2716-:d:1731037
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