Anisotropic liquid drop models-Reference-Cited by-同舟云学术

Anisotropic liquid drop models

Published:2020-03-19 Issue:0 Volume:0 Page:
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Choksi Rustum¹,Neumayer Robin²,Topaloglu Ihsan³^ORCID

Affiliation:

1. Department of Mathematics and Statistics , McGill University , Montréal , QC , Canada

2. Department of Mathematics , Northwestern University , Evanston , IL , USA

3. Department of Mathematics and Applied Mathematics , Virginia Commonwealth University , Richmond , USA

Abstract

Abstract We introduce and study certain variants of Gamow’s liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are established, the shape of minimizers is analyzed. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface energy is isotropic. In sharp contrast, Wulff shapes are the unique minimizers for certain crystalline surface tensions. We also introduce and study several related liquid drop models with anisotropic repulsion for which the Wulff shape is the minimizer in the small mass regime.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2019-0088/pdf

Reference51 articles.

1. E. Acerbi, N. Fusco and M. Morini, Minimality via second variation for a nonlocal isoperimetric problem, Comm. Math. Phys. 322 (2013), no. 2, 515–557.

2. F. J. Almgren, Jr., Some interior regularity theorems for minimal surfaces and an extension of Bernstein’s theorem, Ann. of Math. (2) 84 (1966), 277–292.

3. G. Bellettini, Anisotropic and crystalline mean curvature flow, A Sampler of Riemann–Finsler geometry, Math. Sci. Res. Inst. Publ. 50, Cambridge University, Cambridge (2004), 49–82.

4. G. Bellettini, M. Novaga and M. Paolini, On a crystalline variational problem. I. First variation and global L∞L^{\infty} regularity, Arch. Ration. Mech. Anal. 157 (2001), no. 3, 165–191.

5. G. Bellettini, M. Novaga and M. Paolini, On a crystalline variational problem. II. BV regularity and structure of minimizers on facets, Arch. Ration. Mech. Anal. 157 (2001), no. 3, 193–217.

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