RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Fundam. Prikl. Mat., 1996, Volume 2, Issue 4, Pages 1205–1212 (Mi fpm188)  

The modified Dirichlet problem for the elliptic system of equations that degenerates on the $n$-dimensional sphere and at the origin of coordinates

G. A. Isaeva

Irkutsk State University

Abstract: The belonging of a system of partial differential equations with variable coefficients to one or another homotopic type depends on the domain point at which this system is considered. The degeneration manifolds split the original region into parts. The study of the influence of such degeneration on the solvability character of the boundary value problems is important. We consider the system of $n$ partial second order differential equations
$$ -(x_1^2+x_2^2+\ldots+x_n^2)\Delta u_j+\lambda\frac{\partial}{\partial x_j}\sum_{i=1}^{n}\frac{\partial u_i}{\partial x_i}=0,\quad j=1,\ldots,n, $$
with real parameter $\lambda>0$. This system is elliptic everywhere, except the origin of coordinates and the $n$-dimensional sphere with radius $\sqrt{\lambda}$, on which the parabolic degeneration occurs. We prove that the modified Dirichlet problem for this system considered within a ball that either contains the degeneration sphere or is situated inside it, is solvable, and the solution is unique in the class of bounded functions.

Full text: PDF file (258 kB)

Bibliographic databases:
UDC: 517.956
Received: 01.02.1996

Citation: G. A. Isaeva, “The modified Dirichlet problem for the elliptic system of equations that degenerates on the $n$-dimensional sphere and at the origin of coordinates”, Fundam. Prikl. Mat., 2:4 (1996), 1205–1212

Citation in format AMSBIB
\Bibitem{Isa96}
\by G.~A.~Isaeva
\paper The modified Dirichlet problem for the elliptic system of equations that degenerates on the $n$-dimensional sphere and at the origin of coordinates
\jour Fundam. Prikl. Mat.
\yr 1996
\vol 2
\issue 4
\pages 1205--1212
\mathnet{http://mi.mathnet.ru/fpm188}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1785780}
\zmath{https://zbmath.org/?q=an:0903.35024}


Linking options:
  • http://mi.mathnet.ru/eng/fpm188
  • http://mi.mathnet.ru/eng/fpm/v2/i4/p1205

    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
  • Фундаментальная и прикладная математика
    Number of views:
    This page:155
    Full text:70
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020