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The evolution of H-surfaces with a Plateau boundary condition

By Frank Duzaar and Christoph Scheven

Abstract

In this paper we consider the heat flow associated to the classical Plateau problem for surfaces of prescribed mean curvature. We show that an isoperimetric condition on H ensures the existence of a global weak solution. Moreover, we establish that these global solutions sub-converge, as time tends to infinity, to a conformal solution of the classical Plateau problem for surfaces of prescribed mean curvature

Topics: Mathematics - Analysis of PDEs
Year: 2013
DOI identifier: 10.1016/j.anihpc.2013.10.003
OAI identifier: oai:arXiv.org:1308.1931
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