- Agmon , S. 1975 . Spectral properties of Schrodinger operators and scattering theory . Ann. Scuola Norm. Sup. Pisa , 2 ( 2 ) : 251 – 318 .
- Alber , H.D. 1979 . Estimates for the asymptotic behavior of solutions of the Helmholtz equation with an application to second order elliptic differential operators with variable coefficients . Math.Z. , 167 : 213 – 226 .
- Dassios , G. 1982 . Low frequency scattering theory for a penetrable body with an impenetrable core . SIAM J. Appl. Math. , 42 : 272 – 280 .
- Dassios , G. and Kleinman , R. E. 1989 . On Kelvin inversion and low frequency scattering . SIAM Rev. , 31 : 565 – 585 .
- Gilbarg , D. and Trudinger , N. S. 1977 . Elliptic partial differential equations of second order , New York : Springer, Berlin, Heidelberg .
- Hörmander , L. 1985 . The analysis of linear partial differential operators IV , New York : Springer, Berlin, Heidelberg .
- Ikebe , T. and Saito , Y. 1972 . Limiting absorption method and absolute continuity for the Schrodinger operators . J. Math. Kyoto Univ. , 12 : 513 – 542 .
- Jäger , W. 1967 . Zur Theorie der Schwingungsgleichung mit variablen Koeffizienten in Außengebieten . Math. Z. , 102 : 62 – 88 .
- Leis , R. 1986 . Initial boundary value problems in mathematical physics , Stuttgart : Teubner Wiley .
- Magnus , W. , Oberhettinger , F. and Soni , R. P. 1966 . Formulas and theorems for the special functions of mathematical physics , Berlin, New York : Springer Heidelberg .
- McCamy , R. C. 1965 . Low frequency acoustic oscillations . Quart. Appl. Math. , 23 : 247 – 256 .
- McOwen , R. 1979 . Behavior of the Laplacian in weighted Sobolev spaces . Comm. Pure Appl. Math. , 32 : 783 – 795 .
- McOwen , R. 1981 . Boundary value problems for the Laplacian in an exterior domain . Comm. PDE , 6 : 783 – 798 .
- Muravei , L. A. 1973 . Asymptotic behavior for large values of time of the solutions of the second and third exterior boundary value problems for the wave equation with two spatial variables . Proc. Steklou Inst. Math. , 126 : 77 – 158 .
- Muravei , L. A. 1979 . On the asymptotic behavior, for large values of time, of solutions of exterior boundary value problems for the wave equation with two space variables . Math. USSR Sb. , 35 : 377 – 423 .
- Schechter , M. 1971 . Principles of Functional Analysis , New York : Academic Press .
- Saito , Y. 1971 . The principle of limiting absorption for second order differential equations with operator valued coefficients . Publ. Res. Inst. Math. Sci., Ser. A , 7 : 581 – 619 .
- Shibata , Y. 1983 . On the global existence theorem of classical solutions of second order fully nonlinear hyperbolic equations with first order dissipation in the exterior domain . Tsukuba J. Math. , 7 : 1 – 68 .
- Stuwe , H.-Chr. and Werner , P. 1989 . Remarks on the low frequency asymptotics for the reduced wave equation and the Schrodinger equation in low-dimensional spaces . Asymptotic Analysis , 2 : 179 – 202 .
- Tsutsumi , Y. 1984 . Local energy decay of solutions to the free Schrodinger equation in exterior domains . J. Fac. Sci. Univ. Tokyo, sect. IA, Math. , 31 : 97 – 108 .
- Vainberg , B. R. 1968 . On the analytic properties of the resolvent for a certain class of operator pencils . Math. USSR Sb. , 6 : 241 – 272 .
- Vainberg , B. R. 1973 . On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems . Math. USSR Sb. , 21 : 221 – 239 .
- Vogelsang , V. 1983 . Die Hellichsche Abschatzung fiir die Schwingungsgleichung mit oszillierendem Hauptteil . J. reine angew. Math. , 338 : 109 – 120 .
- Weck , N. and Witsch , K. J. 1991 . Exterior Dirichlet problem for the reduced wave equation: asymptotic analysis of low frequencies . Comm. PDE , 16 : 173 – 195 .
- Weck , N. and Witsch , K. J. 1992 . Exact low frequency analysis for a class of exterior boundary value problems for the reduced wave equation in higher dimensions . Asymptotic Analysis , 6
- Weck , N. and Witsch , K. J. Exact low frequency analysis for a class of exterior boundary value problems for the reduced wave equation in two dimensions . J. DiJ. Equ., ,
- Werner , P. 1985 . Zur Asymptotik der Wellengleichung und der Wärmeleitungsgleichung in zweidimensionalen Außenraumen . Math. Meth. in the Appl. Sci. , 7 : 170 – 201 .
- Werner , P. 1986 . Low frequency asymptotics for the reduced wave equation in twodimensional exterior spaces . Math. Meth. in the Appl. Sci. , 8 : 134 – 156 .
- Wilcox , C. H. 1975 . “ Scattering theory for the d'Alembert equation in exterior domains ” . In Lecture Notes in Mathematics 442 , Berlin, New York : Springer .
Complete Low Frequency Analysis for the Reduced Wave Equation with Variable Coefficients in Three Dimensions *
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