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 Mat. Sb. (N.S.), 1976, Volume 101(143), Number 1(9), Pages 87–130 (Mi msb2955)

Analytic continuations with respect to a parameter of the Green function of exterior boundary value problems for the two-dimensional Helmholtz equation. II

L. A. Muravei

Abstract: This paper gives a construction of some special potentials for the two-dimensional Helmholtz equation. With these potentials, one can establish the existence of Green's functions of exterior boundary-value problems for each $k$ from the complex upper $k$-plane, and the analyticity of these functions in that region. More than that, one can establish the existence of an analytic continuation to the region
$$\{0>\operatorname{Im}k>-\beta(1+|\operatorname{Re}k|^{1/3}, |\operatorname{Re}k|>0\}$$
for some $\beta>0$, with estimates characterizing the behavior of the Green functions for large absolute values of $k$.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1976, 30:1, 77–118

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J05; Secondary 30A14

Citation: L. A. Muravei, “Analytic continuations with respect to a parameter of the Green function of exterior boundary value problems for the two-dimensional Helmholtz equation. II”, Mat. Sb. (N.S.), 101(143):1(9) (1976), 87–130; Math. USSR-Sb., 30:1 (1976), 77–118

Citation in format AMSBIB
\Bibitem{Mur76} \by L.~A.~Muravei \paper Analytic continuations with respect to a~parameter of the Green function of exterior boundary value problems for the two-dimensional Helmholtz equation.~II \jour Mat. Sb. (N.S.) \yr 1976 \vol 101(143) \issue 1(9) \pages 87--130 \mathnet{http://mi.mathnet.ru/msb2955} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=435577} \zmath{https://zbmath.org/?q=an:0335.35033} \transl \jour Math. USSR-Sb. \yr 1976 \vol 30 \issue 1 \pages 77--118 \crossref{https://doi.org/10.1070/SM1976v030n01ABEH001900} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976FJ58100006} 

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This publication is cited in the following articles:
1. L. A. Muravei, “Analytic continuation with respect to a parameter of the Green's functions of exterior boundary value problems for the two-dimensional Helmholtz equation. III”, Math. USSR-Sb., 34:1 (1978), 55–98
2. P. Werner, “Zur Asymptotik der wellengleichung und der wärmeleitungsgleichung in zweidimensionalen außenräumen”, Math Meth Appl Sci, 7:1 (1985), 170
3. Proka D., “Asymptotic Properties of Solutions of Exterior Mixed Problems for the Heat-Conduction Equation”, Differ. Equ., 21:2 (1985), 181–187
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