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 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2013, Volume 25, Issue 2, Pages 63–74 (Mi aa1323)

Research Papers

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

D. E. Apushkinskaya, N. N. Uraltseva

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 $C^{1,1}$.

Keywords: two-phase parabolic obstacle problem, free boundary, optimal regularity.

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English version:
St. Petersburg Mathematical Journal, 2014, 25:2, 195–203

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Citation: D. E. Apushkinskaya, N. N. Uraltseva, “Uniform estimates near the initial state for solutions of the two-phase parabolic problem”, Algebra i Analiz, 25:2 (2013), 63–74; St. Petersburg Math. J., 25:2 (2014), 195–203

Citation in format AMSBIB
\Bibitem{ApuUra13} \by D.~E.~Apushkinskaya, N.~N.~Uraltseva \paper Uniform estimates near the initial state for solutions of the two-phase parabolic problem \jour Algebra i Analiz \yr 2013 \vol 25 \issue 2 \pages 63--74 \mathnet{http://mi.mathnet.ru/aa1323} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3114850} \zmath{https://zbmath.org/?q=an:1304.35144} \elib{http://elibrary.ru/item.asp?id=20730197} \transl \jour St. Petersburg Math. J. \yr 2014 \vol 25 \issue 2 \pages 195--203 \crossref{https://doi.org/10.1090/S1061-0022-2014-01285-X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000343074000003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924352195} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. J. I. Díaz, T. Mingazzini, “Free boundaries touching the boundary of the domain for some reaction-diffusion problems”, Nonlinear Anal., 119 (2015), 275–294
2. D. E. Apushkinskaya, N. N. Uraltseva, “On regularity properties of solutions to the hysteresis-type problem”, Interface Free Bound., 17:1 (2015), 93–115
3. Curran M., Gurevich P., Tikhomirov S., “Recent Advances in Reaction-Diffusion Equations with Non-ideal Relays”, Control of Self-Organizing Nonlinear Systems, Understanding Complex Systems, eds. Scholl E., Klapp SH., Hovel P., Springer-Verlag Berlin, 2016, 211–234
4. D. Apushkinskaya, Free boundary problems. Regularity properties near the fixed boundary, Lect. Notes Math., 2218, Springer, Cham, 2018, xvii+146 pp.
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