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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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

\begin{displaymath}\Delta u-\partial_t u=\chi_\Omega\quad\hbox{in } D\subset\mat... ...,\qquad u=\vert\nabla u\vert=0\quad\hbox{on }D\setminus \Omega \end{displaymath}

with no sign assumptions on $u$ and the time derivative $\partial_t u$.


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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: http://dx.doi.org/10.1090/S0894-0347-04-00466-7
PII: S 0894-0347(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.