This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
The Nonlocal Almgren Problem
Department of Mathematics, Kennesaw State University, Marietta, GA 30060, USA
Mathematics 2025, 13(17), 2716; https://doi.org/10.3390/math13172716 (registering DOI)
Submission received: 18 July 2025
/
Revised: 18 August 2025
/
Accepted: 19 August 2025
/
Published: 23 August 2025
(This article belongs to the Section C: Mathematical Analysis)
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.
Share and Cite
MDPI and ACS Style
Indrei, E. The Nonlocal Almgren Problem. Mathematics 2025, 13, 2716. https://doi.org/10.3390/math13172716
AMA Style
Indrei E. The Nonlocal Almgren Problem. Mathematics. 2025; 13(17):2716. https://doi.org/10.3390/math13172716
Chicago/Turabian StyleIndrei, Emanuel. 2025. "The Nonlocal Almgren Problem" Mathematics 13, no. 17: 2716. https://doi.org/10.3390/math13172716
APA StyleIndrei, E. (2025). The Nonlocal Almgren Problem. Mathematics, 13(17), 2716. https://doi.org/10.3390/math13172716
Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.
