The nonlocal Almgren problem
Analysis of PDEs
2024-08-13 v1 Mathematical Physics
Differential Geometry
math.MP
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 some nonlocal perimeter and convex potential. In the paper, the main result is a quantitative stability theorem for the nonlocal free energy assuming symmetry on the potential. In addition, several results that involve uniqueness, non-existence, and moduli estimates from the theory for crystals are proven also in the nonlocal context.
Cite
@article{arxiv.2408.05675,
title = {The nonlocal Almgren problem},
author = {Emanuel Indrei},
journal= {arXiv preprint arXiv:2408.05675},
year = {2024}
}