Nonlocal variational problems on polygons

Abstract: In this talk I will discuss some recent results regarding the optimality of polygonal shapes for some nonlocal variational problems. In the first part of the talk I will discuss the minimization of an energy functional given by the sum of a crystalline perimeter and a nonlocal interaction of Riesz type: I will exhibit a class of polygonal Wulff shapes which uniquely minimize these energies in the small volume regime. In the second part of the talk I will discuss the optimality of regular polygons for nonlocal energies of generalized Riesz-type in the class of polygons with a fixed number of sides and fixed area, as well as their characterization as unique stationary point. These results are joint work with R. Cristoferi and I. Topaloglu.

mathematical physicsanalysis of PDEsclassical analysis and ODEscategory theorycomplex variablesfunctional analysislogicmetric geometryoptimization and control

Audience: researchers in the topic

VCU ALPS (Analysis, Logic, and Physics Seminar)

Series comments: Description: Research seminar on topics ranging from analysis and logic to mathematical physics.

Meetings will be conducted over Zoom:

Meeting ID: 951 0562 0974

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