The Nonlocal Almgren Problem
Copyright policy )The Nonlocal Almgren Problem
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.
- Kennesaw State University United States
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics, Analysis of PDEs (math.AP)
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