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Mat. Sb. (N.S.), 1982, Volume 118(160), Number 2(6), Pages 236–251 (Mi msb2250)  

This article is cited in 4 scientific papers (total in 4 papers)

An analogue of St. Venant's principle for a polyharmonic equation and applications of it

I. N. Tavkhelidze


Abstract: An a priori energy estimate analogous to the inequalities expressing St. Venant's principle in elasticity theory is obtained for the solution of a polyharmonic equation with the conditions of the first boundary-value problem in an $n$-dimensional domain. These estimates are used to study the behavior of the solution and its derivatives near irregular boundary points and at infinity as a consequence of the geometric properties of the boundary in a neighborhood of these points. Moreover, the estimates obtained are used to prove a uniqueness theorem for the solution of the Dirichlet problem in unbounded domains.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Sbornik, 1983, 46:2, 237–253

Bibliographic databases:

UDC: 517.9
MSC: Primary 31B30, 35B45, 35J40, 73C10; Secondary 35A05, 35J05, 35D99, 34A40, 46E35
Received: 13.03.1981

Citation: I. N. Tavkhelidze, “An analogue of St. Venant's principle for a polyharmonic equation and applications of it”, Mat. Sb. (N.S.), 118(160):2(6) (1982), 236–251; Math. USSR-Sb., 46:2 (1983), 237–253

Citation in format AMSBIB
\Bibitem{Tav82}
\by I.~N.~Tavkhelidze
\paper An analogue of St.\,Venant's principle for a polyharmonic equation and applications of~it
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 118(160)
\issue 2(6)
\pages 236--251
\mathnet{http://mi.mathnet.ru/msb2250}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=658790}
\zmath{https://zbmath.org/?q=an:0522.35016|0497.35011}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 46
\issue 2
\pages 237--253
\crossref{https://doi.org/10.1070/SM1983v046n02ABEH002774}


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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. V. A. Kondrat'ev, O. A. Oleinik, “Boundary-value problems for partial differential equations in non-smooth domains”, Russian Math. Surveys, 38:2 (1983), 1–66  mathnet  crossref  mathscinet  zmath  isi
    2. A. E. Shishkov, “The Phragmén–Lindelöf principle for quasi-linear divergent higher order elliptic equations”, Russian Math. Surveys, 43:4 (1988), 237–238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. S. P. Levashkin, “On the asymptotic properties of generalized solutions of Dirichlet's problem for a polyharmonic equation in non-smooth domains”, Russian Math. Surveys, 44:5 (1989), 208–209  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. G. V. Grishina, “Behavior of solutions of a nonlinear variational problem in a neighborhood of singular points of the boundary and at infinity”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 333–355  mathnet  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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