Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via Symmetrization
Analysis of PDEs
2014-11-11 v1 Optimization and Control
Abstract
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 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 uniqueness of minimizers via an ODE characterization.
Keywords
Cite
@article{arxiv.1411.2579,
title = {Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via Symmetrization},
author = {Eric Baer},
journal= {arXiv preprint arXiv:1411.2579},
year = {2014}
}
Comments
61 pages, 11 figures. To appear in Arch. Ration. Mech. Anal