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St. Petersburg Mathematical Journal

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

 
 

 

Uniform estimates near the initial state for solutions of the two-phase parabolic problem


Authors: D. E. Apushkinskaya and N. N. Uraltseva
Original publication: Algebra i Analiz, tom 25 (2013), nomer 2.
Journal: St. Petersburg Math. J. 25 (2014), 195-203
MSC (2010): Primary 35K05
DOI: https://doi.org/10.1090/S1061-0022-2014-01285-X
Published electronically: March 12, 2014
MathSciNet review: 3114850
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Abstract: Optimal regularity near the initial state is established for weak solutions of the two-phase parabolic obstacle problem. The approach is sufficiently general to allow the initial data to belong to the class $ C^{1,1}$.


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Additional Information

D. E. Apushkinskaya
Affiliation: Department of mathematics and mechanics, St. Petersburg State University, Universitetskii pr. 28, Staryi Peterhof, St. Petersburg 198504, Russia
Email: darya@math.uni-sb.de

N. N. Uraltseva
Affiliation: Department of mathematics and mechanics, St. Petersburg State University, Universitetskii pr. 28, Staryi Peterhof, St. Petersburg 198504, Russia
Email: uraltsev@pdmi.ras.ru

DOI: https://doi.org/10.1090/S1061-0022-2014-01285-X
Keywords: Two-phase parabolic obstacle problem, free boundary, optimal regularity
Received by editor(s): September 27, 2012
Published electronically: March 12, 2014
Additional Notes: Supported by RFBR (grant no. 11-01-00825) and by the St. Petersburg State University Grant. The second author thanks the Alexander von Humboldt Foundation and Saarland University, where this work was done, for hospitality and support.
Dedicated: To the memory of V. S. Buslaev
Article copyright: © Copyright 2014 American Mathematical Society

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