Lipschitz property of the free boundary in the parabolic obstacle problem
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D. E. Apushkinskaya, N. N. Ural′tseva and H. Shahgholian
Translated by: D. E. Apushkinskaya - St. Petersburg Math. J. 15 (2004), 375-391
- DOI: https://doi.org/10.1090/S1061-0022-04-00813-1
- Published electronically: March 25, 2004
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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.References
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Bibliographic 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
- 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.
- © Copyright 2004 American Mathematical Society
- Journal: St. Petersburg Math. J. 15 (2004), 375-391
- MSC (2000): Primary 35R35
- DOI: https://doi.org/10.1090/S1061-0022-04-00813-1
- MathSciNet review: 2052937