A characterization of l1 double bubbles with general interface interaction

Wojciech Górny; Ulisse Stefanelli; Manuel Friedrich

doi:10.48550/arXiv.2311.07782

A characterization of l1 double bubbles with general interface interaction

Wojciech Górny, Ulisse Stefanelli, Manuel Friedrich

Department of Mathematics

Publications: Working paper › Preprint

Abstract

We investigate the optimal arrangements of two planar sets of given volume which are minimizing the l1 double-bubble interaction functional. The latter features a competition between the minimization of the l1 perimeters of the two sets and the maximization of their l1 interface. We investigate the problem in its full generality for sets of finite perimeter, by considering the whole range of possible interaction intensities and all relative volumes of the two sets. The main result is the complete classification of minimizers.

Original language	English
DOIs	https://doi.org/10.48550/arXiv.2311.07782
Publication status	Published - 13 Nov 2023

Austrian Fields of Science 2012

101002 Analysis
101016 Optimisation
101009 Geometry

Keywords

double bubbles
anisotropic perimeter
interfaces

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10.48550/arXiv.2311.07782

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abstract = "We investigate the optimal arrangements of two planar sets of given volume which are minimizing the l1 double-bubble interaction functional. The latter features a competition between the minimization of the l1 perimeters of the two sets and the maximization of their l1 interface. We investigate the problem in its full generality for sets of finite perimeter, by considering the whole range of possible interaction intensities and all relative volumes of the two sets. The main result is the complete classification of minimizers. ",

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AU - Friedrich, Manuel

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N2 - We investigate the optimal arrangements of two planar sets of given volume which are minimizing the l1 double-bubble interaction functional. The latter features a competition between the minimization of the l1 perimeters of the two sets and the maximization of their l1 interface. We investigate the problem in its full generality for sets of finite perimeter, by considering the whole range of possible interaction intensities and all relative volumes of the two sets. The main result is the complete classification of minimizers.

AB - We investigate the optimal arrangements of two planar sets of given volume which are minimizing the l1 double-bubble interaction functional. The latter features a competition between the minimization of the l1 perimeters of the two sets and the maximization of their l1 interface. We investigate the problem in its full generality for sets of finite perimeter, by considering the whole range of possible interaction intensities and all relative volumes of the two sets. The main result is the complete classification of minimizers.

KW - double bubbles

KW - anisotropic perimeter

KW - interfaces

U2 - 10.48550/arXiv.2311.07782

DO - 10.48550/arXiv.2311.07782

M3 - Preprint

BT - A characterization of l1 double bubbles with general interface interaction

ER -

A characterization of l1 double bubbles with general interface interaction

Abstract

Austrian Fields of Science 2012

Keywords

Access to Document

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Cite this