Regularity of a free boundary in parabolic potential theory

Authors:
Luis Caffarelli, Arshak Petrosyan and Henrik Shahgholian

Journal:
J. Amer. Math. Soc. **17** (2004), 827-869

MSC (2000):
Primary 35R35

Published electronically:
August 27, 2004

MathSciNet review:
2083469

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the regularity of the free boundary in a Stefan-type problem

with no sign assumptions on and the time derivative .

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Additional Information

**Luis Caffarelli**

Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

Email:
caffarel@math.utexas.edu

**Arshak Petrosyan**

Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

Address at time of publication:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Email:
arshak@math.utexas.edu, arshak@math.purdue.edu

**Henrik Shahgholian**

Affiliation:
Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

Email:
henriksh@math.kth.se

DOI:
https://doi.org/10.1090/S0894-0347-04-00466-7

Keywords:
Free boundary problems,
Stefan problem,
regularity,
global solutions,
monotonicity formulas.

Received by editor(s):
December 20, 2002

Published electronically:
August 27, 2004

Additional Notes:
The first author was supported in part by the NSF

The second author thanks the Göran Gustafsson Foundation and the Department of Mathematics, Royal Institute of Technology, for the visiting appointment

The third author was supported in part by the Swedish Research Council

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.