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Mathematics of the USSR-Sbornik, 1988, Volume 61, Issue 2, Pages 495–527
DOI: https://doi.org/10.1070/SM1988v061n02ABEH003221
(Mi sm2626)
 

This article is cited in 1 scientific paper (total in 1 paper)

Some boundary value problems for elliptic equations, and the Lie algebras connected with them. II

B. P. Paneah
References:
Abstract: This article presents detailed results on solvability and regularity of solutions for the noncoercive boundary value problem $lu=f$ in $\Omega$, $Au=g$ on $\partial\Omega$, where $l$ is a second-order elliptic operator in a bounded region $\Omega\subset\mathbf R^{n+1}$, and $A$ is a second-order operator for which the Lopatinskii conditions are violated on a sufficiently arbitrary subset of $\partial\Omega$. In particular, the principal part of $A$ need not be of definite sign on $T^*(\partial\Omega)$, and this leads (with a view to obtaining well-posed formulations) to the additional condition $u=h$ on $\mu_1$ and to the allowance of a finite discontinuity of $u|_{\partial\Omega}$ on $\mu_2$, where $\mu_1$ and $\mu_2$ are submanifolds of $\partial\Omega$ of codimension 1. The paper encompasses a large part of the known results on the degenerate oblique derivative problem.
Bibliography: 10 titles.
Received: 27.05.1986
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1987, Volume 133(175), Number 4(8), Pages 508–538
Bibliographic databases:
UDC: 517.95
MSC: Primary 35J25, 35A05; Secondary 35R25, 35J70, 35B45, 35S15
Language: English
Original paper language: Russian
Citation: B. P. Paneah, “Some boundary value problems for elliptic equations, and the Lie algebras connected with them. II”, Mat. Sb. (N.S.), 133(175):4(8) (1987), 508–538; Math. USSR-Sb., 61:2 (1988), 495–527
Citation in format AMSBIB
\Bibitem{Pan87}
\by B.~P.~Paneah
\paper Some boundary value problems for elliptic equations, and the Lie algebras connected with them.~II
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 133(175)
\issue 4(8)
\pages 508--538
\mathnet{http://mi.mathnet.ru/sm2626}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=911806}
\zmath{https://zbmath.org/?q=an:0686.35036|0658.35028}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 61
\issue 2
\pages 495--527
\crossref{https://doi.org/10.1070/SM1988v061n02ABEH003221}
Linking options:
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  • https://doi.org/10.1070/SM1988v061n02ABEH003221
  • https://www.mathnet.ru/eng/sm/v175/i4/p508
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    This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:268
    Russian version PDF:91
    English version PDF:6
    References:52
     
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