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Mat. Zametki, 1997, Volume 61, Issue 5, Pages 759–768 (Mi mz1558)  

Integral estimates of the solutions to the Helmholtz equation in unbounded domains

A. V. Filinovskii

N. E. Bauman Moscow State Technical University

Abstract: The following boundary value problem is studied:
$$ \begin{gathered} \Delta v+\omega^2v=h(x),\qquad x\in\Omega\subset{\mathbb R}^n,\quad n\ge2,\qquad-\infty<\omega<+\infty, \quad v|_\Gamma=0,\quad\Gamma=\partial\Omega, \end{gathered} $$
here the surface $\Gamma$ satisfies the condition $(\nu,\nabla\varphi(x))|_\Gamma\le0$, where
$$ \varphi(x)=\sum_{j=1}^n\alpha_jx_j^2,\qquad 0<\alpha_1\le\alpha_1\le…\le\alpha_n=1, $$
and $\nu$ is the outward (with respect to $\Omega$) normal to $\Gamma$.

DOI: https://doi.org/10.4213/mzm1558

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English version:
Mathematical Notes, 1997, 61:5, 635–643

Bibliographic databases:

UDC: 517.947.4
Received: 14.07.1995

Citation: A. V. Filinovskii, “Integral estimates of the solutions to the Helmholtz equation in unbounded domains”, Mat. Zametki, 61:5 (1997), 759–768; Math. Notes, 61:5 (1997), 635–643

Citation in format AMSBIB
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\by A.~V.~Filinovskii
\paper Integral estimates of the solutions to the Helmholtz equation in unbounded domains
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 5
\pages 759--768
\mathnet{http://mi.mathnet.ru/mz1558}
\crossref{https://doi.org/10.4213/mzm1558}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1620149}
\zmath{https://zbmath.org/?q=an:0915.35017}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 5
\pages 635--643
\crossref{https://doi.org/10.1007/BF02355086}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997YE52200014}


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