Existence of translating solutions to the flow by powers of mean curvature on unbounded domains

Details Existence of translating solutions to the flow by powers of mean curvature on unbounded domains Existence of translating solutions to the flow by powers of mean curvature on unbounded domains

2010-09-16

arxiv.org/abs/1009.3115v1

Mathematics

Analysis of PDEs

30 pages

Scientific paper

In this paper, we prove the existence of classical solutions of the Dirichlet problem for a class of quasi-linear elliptic equations on unbounded domains like a cone or a U-type domain. This problem comes from the study of mean curvature flow and its generalization, the flow by powers of mean curvature. Our approach is a modified version of the classical Perron method, where the solutions to the minimal surface equation are used as sub-solutions and a family auxiliary functions are constructed as super-solutions.

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