Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||17|
|Published online||01 March 2021|
On minimizers of an anisotropic liquid drop model
Department of Mathematics and Applied Mathematics, Virginia Commonwealth University,
* Corresponding author: firstname.lastname@example.org
Accepted: 7 October 2020
We consider a variant of Gamow’s liquid drop model with an anisotropic surface energy. 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. We show that for smooth anisotropies, in the small nonlocality regime, minimizers converge to the Wulff shape in C1-norm and quantify the rate of convergence. We also obtain a quantitative expansion of the energy of any minimizer around the energy of a Wulff shape yielding a geometric stability result. For certain crystalline surface tensions we can determine the global minimizer and obtain its exact energy expansion in terms of the nonlocality parameter.
Mathematics Subject Classification: 35Q40 / 35Q70 / 49Q20 / 49S05 / 82D10
Key words: Liquid drop model / anisotropic / Wulff shape / quasi-minimizers of anisotropic perimeter
© EDP Sciences, SMAI 2021
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