Minimality of polytopes in a nonlocal anisotropic isoperimetric problem
| Autor: | Marco Bonacini, Ihsan Topaloglu, Riccardo Cristoferi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis Regular polygon Polytope Computer Science::Computational Geometry 01 natural sciences 010101 applied mathematics Perimeter Rigidity (electromagnetism) Mathematics - Analysis of PDEs 49Q10 49Q20 49J10 49K21 FOS: Mathematics Minification 0101 mathematics Isoperimetric inequality Anisotropy Analysis Mathematics Analysis of PDEs (math.AP) Energy functional |
| Zdroj: | Nonlinear Analysis, 205, pp. 1-19 Nonlinear Analysis, 205, 1-19 |
| ISSN: | 0362-546X |
| DOI: | 10.1016/j.na.2020.112223 |
| Popis: | We consider the minimization of an energy functional given by the sum of a crystalline perimeter and a nonlocal interaction of Riesz type, under volume constraint. We show that, in the small mass regime, if the Wulff shape of the anisotropic perimeter has certain symmetry properties, then it is the unique global minimizer of the total energy. In dimension two this applies to convex polygons which are reflection symmetric with respect to the bisectors of the angles. We further prove a rigidity result for the structure of (local) minimizers in two dimensions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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