The double queen Dido's problem
| Autor: | Shigeru Sakaguchi, Antoine Henrot, Lorenzo Cavallina |
|---|---|
| Přispěvatelé: | Research Center for Pure and Applied Mathematics, GSIS, Tohoku University (GSIS Mathematics), Tohoku University [Sendai], Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), This research was partially supported by the Grants-in-Aid for Scientific Research (B) No.18H01126 and JSPS Fellows No.18J11430 of Japan Society for the Promotion of Science., ANR-18-CE40-0013,SHAPO,Optimisation de forme(2018) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Dido's problem Dimension (graph theory) AMS subject classifications : 49Q20 two-phase 01 natural sciences Omega constrained minimization problem Combinatorics 0103 physical sciences FOS: Mathematics 0101 mathematics [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG] Mathematics 010102 general mathematics 49Q20 Constraint (information theory) Discontinuity (linguistics) Differential geometry Hyperplane Differential Geometry (math.DG) Isoperimetric problem Piecewise weighted manifold 010307 mathematical physics Geometry and Topology [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Isoperimetric inequality |
| Zdroj: | The Journal of Geometric Analysis The Journal of Geometric Analysis, Springer, In press, ⟨10.1007/s12220-020-00549-1⟩ |
| ISSN: | 1050-6926 1559-002X |
| Popis: | This paper deals with a variation of the classical isoperimetric problem in dimension $N\ge 2$ for a two-phase piecewise constant density whose discontinuity interface is a given hyperplane. We introduce a weighted perimeter functional with three different weights, one for the hyperplane and one for each of the two open half-spaces in which $\mathbb{R}^N$ gets partitioned. We then consider the problem of characterizing the sets $\Omega$ that minimize this weighted perimeter functional under the additional constraint that the volumes of the portions of $\Omega$ in the two half-spaces are given. It is shown that the problem admits two kinds of minimizers, which will be called type I and type II, respectively. These minimizers are made of the union of two spherical domes whose angle of incidence satisfies some kind of \textquotedblleft Snell's law\textquotedblright. Finally, we provide a complete classification of the minimizers depending on the various parameters of the problem. Comment: 20 pages, 4 figures |
| Databáze: | OpenAIRE |
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