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

2010/09/16 by Huai-Yu Jian, Jian, Huai-Yu, Hong-Jie Ju +1
Mathematics · #35J60 #52C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:35J60 #msc:52C44

paper · pdf · doi:10.48550/arxiv.1009.3115

30 pages

arxiv created 2010/09/16 · arxiv updated 2010/09/17

Abstract

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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