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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Lipschitz property of the free boundary in the parabolic obstacle problem


Authors: D. E. Apushkinskaya, N. N. Ural'tseva and H. Shahgholian
Translated by: D. E. Apushkinskaya
Original publication: Algebra i Analiz, tom 15 (2003), nomer 3.
Journal: St. Petersburg Math. J. 15 (2004), 375-391
MSC (2000): Primary 35R35
Published electronically: March 25, 2004
MathSciNet review: 2052937
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Abstract: A parabolic obstacle problem with zero constraint is considered. It is proved, without any additional assumptions on a free boundary, that near the fixed boundary where the homogeneous Dirichlet condition is fulfilled, the boundary of the noncoincidence set is the graph of a Lipschitz function.


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Additional Information

D. E. Apushkinskaya
Affiliation: Saarland University, Saarbrücken, Germany
Email: darya@math.uni-sb.de

N. N. Ural'tseva
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: uunur@nur.usr.pu.ru

H. Shahgholian
Affiliation: Royal Institute of Technology, Stockholm, Sweden
Email: henriks@math.kth.se

DOI: https://doi.org/10.1090/S1061-0022-04-00813-1
Keywords: Free boundary problems, regularity, parabolic variational inequality
Received by editor(s): February 18, 2003
Published electronically: March 25, 2004
Additional Notes: D. E. Apushkinskaya and N. N. Ural′tseva were partially supported by the Russian Foundation for Basic Research (grant no. 02-01-00276). H. Shahgholian was partially supported by the Swedish Natural Sciences Research Council.
Article copyright: © Copyright 2004 American Mathematical Society