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

Published electronically:
March 12, 2014

MathSciNet review:
3114850

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Abstract | References | Similar Articles | Additional Information

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 .

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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