Regularity of a free boundary in parabolic potential theory
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- by Luis Caffarelli, Arshak Petrosyan and Henrik Shahgholian
- J. Amer. Math. Soc. 17 (2004), 827-869
- DOI: https://doi.org/10.1090/S0894-0347-04-00466-7
- Published electronically: August 27, 2004
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Abstract:
We study the regularity of the free boundary in a Stefan-type problem \[ \Delta u - \partial _t u = \chi _\Omega \quad \text {in $D\subset \mathbb {R}^n\times \mathbb {R}$}, \qquad u = |\nabla u| = 0 \quad \text {on $D\setminus \Omega $} \] with no sign assumptions on $u$ and the time derivative $\partial _t u$.References
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Bibliographic Information
- Luis Caffarelli
- Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
- MR Author ID: 44175
- 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
- MR Author ID: 654444
- 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
- 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 - © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 17 (2004), 827-869
- MSC (2000): Primary 35R35
- DOI: https://doi.org/10.1090/S0894-0347-04-00466-7
- MathSciNet review: 2083469