Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via Symmetrization
arXiv:1411.2579 · doi:10.1007/s00205-014-0788-z
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.
61 pages, 11 figures. To appear in Arch. Ration. Mech. Anal