Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via Symmetrization
We consider a variational model describing the shape of liquid drops and crystals under the influence of gravity, resting on a horizontal surface. Making use of anisotropic symmetrization techniques, we establish the existence, convexity and symmetry of minimizers for a class of surface tensions adm...
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/104380 https://orcid.org/0000-0002-8283-8661 |
| Summary: | We consider a variational model describing the shape of liquid drops and crystals under the influence of gravity, resting on a horizontal surface. Making use of anisotropic symmetrization techniques, we establish the existence, convexity and symmetry of minimizers for a class of surface tensions admissible to the symmetrization procedure. In the case of smooth surface tensions, we obtain the uniqueness of minimizers via an ODE characterization. |
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