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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Regularity of a free boundary in parabolic potential theory
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by Luis Caffarelli, Arshak Petrosyan and Henrik Shahgholian PDF
J. Amer. Math. Soc. 17 (2004), 827-869 Request permission

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 $\partial _t u$.
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Additional 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