Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via Symmetrization
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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.
Date issued
2014-08Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Archive for Rational Mechanics and Analysis
Publisher
Springer Berlin Heidelberg
Citation
Baer, Eric. “Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via Symmetrization.” Archive for Rational Mechanics and Analysis 215.2 (2015): 531–578.
Version: Author's final manuscript
ISSN
0003-9527
1432-0673