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arXiv · 1009.3115

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

Huai-Yu Jian·Hong-Jie Ju
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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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Huai-Yu Jian, Hong-Jie Ju. 2010-09-16. Existence of translating solutions to the flow by powers of mean curvature on unbounded domains. https://arxiv.org/abs/1009.3115

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