Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zapiski Nauchnykh Seminarov POMI, 2000, Volume 271, Pages 39–55 (Mi znsl1346)  

This article is cited in 14 scientific papers (total in 15 papers)

Boundary estimates for solutions to the parabolic free boundary problem

D. E. Apushkinskayaa, H. Shahgholianb, N. N. Ural'tsevaa

a Saint-Petersburg State University
b Royal Institute of Technology
Abstract: Let $u$ and $\varOmega$ (an open set in $\mathbb R^{n+1}_+=\{(x,t):x\in\mathbb R^n,\ t\in\mathbb R^1,\ x_1>0\}$, $n\geqslant2$) solve the following problem:
$$ H(u)=\chi_{\varOmega}, \quad u=|Du|=0 \quad\text{in}\quad Q_1^+\setminus\varOmega, \quad u=0 \quad\text{on}\quad \Pi\cap Q_1, $$
where $H=\Delta-\partial_t$ is the heat operator, $\chi_{\varOmega}$ denotes the characteristic function of $\varOmega$, $Q_1$ is the unit cylinder in $\mathbb R^{n+1}$, $Q_1^+=Q_1\cap\mathbb R^{n+1}_+$, $\Pi=\{(x,t):x_1=0\}$, and the first equation is satisfied in the sense of distributions. We obtain the optimal regularity of the function $u$, i.e., we show that $u\in C^{1,1}_x\cap C^{0,1}_t$.
Received: 16.10.2000
English version:
Journal of Mathematical Sciences (New York), 2003, Volume 115, Issue 6, Pages 2720–2730
DOI: https://doi.org/10.1023/A:1023357416587
Bibliographic databases:
UDC: 517.9
Language: English
Citation: D. E. Apushkinskaya, H. Shahgholian, N. N. Ural'tseva, “Boundary estimates for solutions to the parabolic free boundary problem”, Boundary-value problems of mathematical physics and related problems of function theory. Part 31, Zap. Nauchn. Sem. POMI, 271, POMI, St. Petersburg, 2000, 39–55; J. Math. Sci. (N. Y.), 115:6 (2003), 2720–2730
Citation in format AMSBIB
\Bibitem{ApuShaUra00}
\by D.~E.~Apushkinskaya, H.~Shahgholian, N.~N.~Ural'tseva
\paper Boundary estimates for solutions to the parabolic free boundary problem
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~31
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 271
\pages 39--55
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1346}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1810607}
\zmath{https://zbmath.org/?q=an:1031.35150}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 115
\issue 6
\pages 2720--2730
\crossref{https://doi.org/10.1023/A:1023357416587}
Linking options:
  • https://www.mathnet.ru/eng/znsl1346
  • https://www.mathnet.ru/eng/znsl/v271/p39
  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:258
    Full-text PDF :98
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024