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.), 1981, Volume 116(158), Number 1(9), Pages 72–86 (Mi msb2432)  

This article is cited in 6 scientific papers (total in 6 papers)

Some singularities in the behavior of solutions of equations of minimal-surface type in unbounded domains

V. M. Miklyukov


Abstract: In this paper the behavior of the solutions of equations of minimal-surface type is studied in unbounded domains. It is established that if the domain is sufficiently narrow in the neighborhood of the point at infinity of $\mathbf R^2$, then any solution having zero Dirichlet or Neumann data on the boundary must be identically constant. A condition on the narrowness of the domain is found under which the solution cannot change sign in the domain. An estimate of the form $\sum_ki(a_k)\leqslant c$ is proved, where $i(a_k)$ is the topological index of the solution at the point $a_k$, $c$ is a constant depending only on the equation, the domain and the number of points of local extremum of the boundary function, and the summation is taken over all critical points of the solution.
Bibliography: 11 titles.

Full text: PDF file (1456 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1983, 44:1, 61–73

Bibliographic databases:

UDC: 517.54+517.947
MSC: Primary 35J20; Secondary 49F10, 53A10
Received: 10.11.1980

Citation: V. M. Miklyukov, “Some singularities in the behavior of solutions of equations of minimal-surface type in unbounded domains”, Mat. Sb. (N.S.), 116(158):1(9) (1981), 72–86; Math. USSR-Sb., 44:1 (1983), 61–73

Citation in format AMSBIB
\Bibitem{Mik81}
\by V.~M.~Miklyukov
\paper Some singularities in the behavior of solutions of equations of minimal-surface type in unbounded domains
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 1(9)
\pages 72--86
\mathnet{http://mi.mathnet.ru/msb2432}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=632489}
\zmath{https://zbmath.org/?q=an:0556.49022|0495.49028}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 1
\pages 61--73
\crossref{https://doi.org/10.1070/SM1983v044n01ABEH000951}


Linking options:
  • http://mi.mathnet.ru/eng/msb2432
  • http://mi.mathnet.ru/eng/msb/v158/i1/p72

    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. Vuorinen M., “Conformal Geometry and Quasiregular-Mappings”, Lect. Notes Math., 1319 (1988), 1–&  crossref  mathscinet  zmath  isi
    2. V. M. Miklyukov, “Some criteria for parabolicity and hyperbolicity of the boundary sets of surfaces”, Izv. Math., 60:4 (1996), 763–809  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Hwang J., “How Many Theorems Can Be Derived From a Vector Function - on Uniqueness Theorems for the Minimal Surface Equation”, Taiwan. J. Math., 7:4 (2003), 513–539  mathscinet  zmath  isi
    4. Meeks Iii W.H., Perez J., “The Classical Theory of Minimal Surfaces”, Bull. Amer. Math. Soc., 48:3 (2011), 325–407  crossref  mathscinet  zmath  isi  elib
    5. Allen Weitsman, “Spiraling Minimal Graphs”, Comput. Methods Funct. Theory, 2014  crossref
    6. Erik Lundberg, Allen Weitsman, “On the growth of solutions to the minimal surface equation over domains containing a halfplane”, Calc. Var, 2015  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:254
    Full text:98
    References:29

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