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Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via Symmetrization (1411.2579v1)
Published 10 Nov 2014 in math.AP and math.OC
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.
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