Short-Time Regularity for the H-Surface Flow

descriptionPublicationkeyboard_double_arrow_right Article 27 Mar 2014 Germany English Publisher:Oxford University Press (OUP)Journal:International Mathematics Research Notices (issn: 1073-7928, eissn: 1687-0247,

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Authors: Bögelein, Verena; Duzaar, Frank; Scheven, Christoph;

doi: 10.1093/imrn/rnu042

Short-Time Regularity for the H-Surface Flow

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Abstract

We consider the heat flow associated with the H-surface system given by ∂tu−Δuu(⋅,0)=−2(H∘u)D1u×D2uon B×(0,∞),=uo on B,u=g on ∂B×(0,∞), for a prescribed bounded and continuous function H:R3→R satisfying an isoperimetric condition of type c for 00. From this, we deduce the existence of a global solution u~:B×(0,∞)→R3 that is regular except from finitely many singular times.

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Germany

Related Organizations

University of Duisburg-Essen
Germany
University of Erlangen-Nuremberg
Germany

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DDC Classification::5 Naturwissenschaften und Mathematik :: 51 Mathematik :: 510 Mathematik, Mathematik

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