Vol. 5, No. 5, 2012

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The two-phase Stefan problem: regularization near Lipschitz initial data by phase dynamics

Sunhi Choi and Inwon Kim

Vol. 5 (2012), No. 5, 1063–1103
Abstract

In this paper we investigate the regularizing behavior of two-phase Stefan problem near initial Lipschitz data. A description of the regularizing phenomena is given in terms of the corresponding space-time scale.

Keywords
free boundary problem, Stefan problem, phase transition, regularity near initial data, viscosity solutions
Mathematical Subject Classification 2010
Primary: 35K55, 35R35, 76D27
Milestones
Received: 6 February 2011
Revised: 12 October 2011
Accepted: 15 January 2012
Published: 29 December 2012
Authors
Sunhi Choi
Department of Mathematics
University of Arizona
Tucson, AZ 85721
United States
Inwon Kim
Department of Mathematics
UCLA
Los Angeles, CA 90095
United States