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Lipschitz property of the free boundary in the parabolic obstacle problem
Author(s):
D.
E.
Apushkinskaya;
N.
N.
Ural'tseva;
H.
Shahgholian
Translated by:
D. E. Apushkinskaya
Original publication:
Algebra i Analiz,
tom 15
(2003),
vypusk 3.
Journal:
St. Petersburg Math. J.
15
(2004),
375-391.
MSC (2000):
Primary 35R35
Posted:
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.
References:
-
- [AUS1]
- D. E. Apushkinskaya, N. N. Ural'tseva, and H. Shahgholian, Boundary estimates for solutions to the parabolic free boundary problem, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 271 (2000), 39-55. (English) MR 2002b:35205
- [AUS2]
- -, On the global solutions of the parabolic obstacle problem, Algebra i Analiz 14 (2002), no. 1, 3-25; English transl., St. Petersburg Math. J. 14 (2003), no. 1, 1-17. MR 2003d:35163
- [AtSa]
- I. Athanasopoulos and S. Salsa, An application of a parabolic comparison principle to free boundary problems, Indiana Univ. Math. J. 40 (1991), no. 1, 29-32. MR 92d:35306
- [C1]
- L. A. Caffarelli, The regularity of free boundaries in higher dimensions, Acta Math. 139 (1977), 155-184. MR 56:12601
- [C2]
- -, A monotonicity formula for heat functions in disjoint domains, Boundary Value Problems for Partial Differential Equations and Applications, RMA Res. Notes Appl. Math., vol. 29, Masson, Paris, 1993, pp. 53-60. MR 95e:35096
- [CK]
- L. A. Caffarelli and C. Kenig, Gradient estimates for variable coefficient parabolic equations and singular perturbation problems, Amer. J. Math. 120 (1998), no. 2, 391-440. MR 99b:35081
- [CPS]
- L. A. Caffarelli, A. Petrosyan, and H. Shahgholian, Regularity of a free boundary in parabolic potential theory (in preparation).
- [W]
- G. S. Weiss, Self-similar blow-up and Hausdorff dimension estimates for a class of parabolic free boundary problems, SIAM J. Math. Anal. 30 (1999), no. 3, 623-644. MR 2000d:35267
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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:
10.1090/S1061-0022-04-00813-1
PII:
S 1061-0022(04)00813-1
Keywords:
Free boundary problems,
regularity,
parabolic variational inequality
Received by editor(s):
18/FEB/2003
Posted:
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 of article:
Copyright
2004,
American Mathematical Society
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