Matematicheskii Sbornik. Novaya Seriya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb. (N.S.), 1976, Volume 99(141), Number 2, Pages 282–294 (Mi msb2745)  

This article is cited in 8 scientific papers (total in 8 papers)

On an estimate of the Dirichlet integral in unbounded domains

A. K. Gushchin


Abstract: For an arbitrary unbounded region $\Omega$ satisfying a certain condition ($\operatorname{meas}\Omega=\infty$, and $\Omega$ can be such that
$$ \lim_{R\to\infty}\frac1R\operatorname{meas}(\Omega\cap\{|x|<R\})=0) $$
a lower bound for the Dirichlet integral $\int_\Omega|\nabla f(x)|^2 dx$ is established for all functions $f(x)$ in $W_2^1(\Omega)\cap L_r(\Omega)$ which have finite moment $\mu_l=\int_\Omega|x| |f(x)|^l dx$, $0<l<2<r$. The bound of the Dirichlet integral is a positive function of the variables $\mu_l$, $\|f\|_{L_r(\Omega)}$, $\|f\|_{L_2(\Omega)}$ and $\|f\|_{L_q(\Omega)}$, $q\geqslant1$, $l\leqslant q<2$, and is determined by certain geometric characteristics of $\Omega$.
Bibliography: 4 titles.

Full text: PDF file (1082 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1976, 28:2, 249–261

Bibliographic databases:

UDC: 517.5
MSC: Primary 26A86; Secondary 35K20, 35A15
Received: 26.06.1975

Citation: A. K. Gushchin, “On an estimate of the Dirichlet integral in unbounded domains”, Mat. Sb. (N.S.), 99(141):2 (1976), 282–294; Math. USSR-Sb., 28:2 (1976), 249–261

Citation in format AMSBIB
\Bibitem{Gus76}
\by A.~K.~Gushchin
\paper On an estimate of the Dirichlet integral in unbounded domains
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 99(141)
\issue 2
\pages 282--294
\mathnet{http://mi.mathnet.ru/msb2745}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=626999}
\zmath{https://zbmath.org/?q=an:0338.35009}
\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 2
\pages 249--261
\crossref{https://doi.org/10.1070/SM1976v028n02ABEH001650}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976EM69100008}


Linking options:
  • http://mi.mathnet.ru/eng/msb2745
  • http://mi.mathnet.ru/eng/msb/v141/i2/p282

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. K. Gushchin, “Stabilization of the solutions of the second boundary value problem for a second order parabolic equation”, Math. USSR-Sb., 30:4 (1976), 403–440  mathnet  crossref  mathscinet  zmath  isi
    2. A. K. Guščin, “On the behaviour ast→∞ of solutions of the second mixed problem for a second-order parabolic equation”, Appl Math Optim, 6:1 (1980), 169  crossref  mathscinet  isi
    3. V. I. Ushakov, “Stabilization of solutions of the third mixed problem for a second order parabolic equation in a noncylindrical domain”, Math. USSR-Sb., 39:1 (1981), 87–105  mathnet  crossref  mathscinet  zmath  isi
    4. A. K. Gushchin, “On the uniform stabilization of solutions of the second mixed problem for a parabolic equation”, Math. USSR-Sb., 47:2 (1984), 439–498  mathnet  crossref  mathscinet  zmath
    5. A. I. Ibragimov, “Some qualitative properties of solutions of the mixed problem for equations of elliptic type”, Math. USSR-Sb., 50:1 (1985), 163–176  mathnet  crossref  mathscinet  zmath
    6. A. K. Gushchin, V. P. Mikhailov, Yu. A. Mikhailov, “On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation”, Math. USSR-Sb., 56:1 (1987), 141–162  mathnet  crossref  mathscinet  zmath
    7. Lezhnev A., “Bounds of Green-Function and Solutions of a 2nd Mixed Problem for a Parabolic Equation”, Differ. Equ., 25:4 (1989), 478–486  mathnet  mathscinet  zmath  isi
    8. Andreucci D., Tedeev A., “Optimal Bounds and Blow Up Phenomena for Parabolic Problems in Narrowing Domains”, Proc. R. Soc. Edinb. Sect. A-Math., 128:Part 6 (1998), 1163–1180  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:250
    Full text:76
    References:33
    First page:2

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021