Anisotropic liquid drop models
| Autor: | Rustum Choksi, Ihsan Topaloglu, Robin Neumayer |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Surface (mathematics)
Applied Mathematics Mathematical analysis Isotropy Liquid drop FOS: Physical sciences Mathematical Physics (math-ph) Surface energy Surface tension Mathematics - Analysis of PDEs Semi-empirical mass formula FOS: Mathematics Mathematics::Differential Geometry Anisotropy 35Q40 35Q70 49Q20 49S05 82D10 Analysis Geometry and topology Mathematical Physics Mathematics Analysis of PDEs (math.AP) |
| Popis: | 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. This version will appear in Adv. Calc. Var |
| Databáze: | OpenAIRE |
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