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Surface gradients and continuity properties for some integral operators in classical scattering theory. (English) Zbl 0692.35073
From the author’s abstract. The surface gradients of some of the most important boundary integral operators for the time-harmonic Helmholtz and Maxwell equations are computed. The results are used to give new and elementary proofs of the continuity properties of these boundary operators in Sobolev and Hölder spaces of arbitrary order.
Reviewer: T.R.Faulkner

MSC:
35P25 Scattering theory for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
45A05 Linear integral equations
35Q99 Partial differential equations of mathematical physics and other areas of application
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[1] Sobolev spaces, Academic Press, New York, 1975. · Zbl 0314.46030
[2] Agmon, Comm. Pure Appl. Math. 12 pp 623– (1959)
[3] and , Introduction to the Theory of Partial Differential Equations, North Holland, Amsterdam, 1982,
[4] and , Integral Equation Methods in Scattering Theory, Wiley, new York, 1983.
[5] Die Potentialtheorie und ihre Anwendungen auf Grundaufgaben der mathematischen Physik, Teubner Verlag, Leipzig. 1957. · Zbl 0077.09702
[6] Hsiao, J. Math. Anal. Appl. 58 pp 449– (1977)
[7] Lineare Integraloperatoren, Teubner Verlag, Stuttgart, 1970.
[8] Foundations of Potentials Theory, Springer Verlag, Berlin, 1967.
[9] ’Generalized boundary value- and control problems for the Helmholtz equation’, Habilitation thesis, Göttingen 1984.
[10] Randwertaufgaben der Schwingungstheorie und Integralgleichungen, D. Verl. d. W., 1956.
[11] , and , Three-dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North Holland, Amsterdam, 1979.
[12] Lax, Comm. Pure Appl. Math. 7 pp 633– (1954)
[13] Vorlesungen über partielle Differentialgleichungen zweiter Ordnung, Bibliographisches Institut, Mannheim, 1967.
[14] and , Problémes aux Limites non Homogénes et Application, Vol. 1, Dunod, Paris, 1968.
[15] Potentialtheorie, Teubner, Stuttgart, 1968.
[16] and Singuläre Integralgleichungen, Akademic-Verlag, Berlin, 1980.
[17] Grundprobleme der mathematischen Theorie elektromagnetischer Schwingungen, Springer Verlag, Berlin, 1957.
[18] Les Méthodes Directes en Théorie des Équations Elliptiques, Masson, Paris, 1967.
[19] ’Topics in pseudo-differential operators’, in (ed.) Pseudo-Differential Operators, CIME, Roma, Cremonese, 1969.
[20] Lineare Operatoren in Hilberträumen, Teubner Verlag, Stuttgart, 1976.
[21] Boundary Element Methods and Their Asymptotic Convergence. CISM Courses 277, Springer-Verlag, Wien, New York, 1983. · Zbl 0618.65109
[22] Werner, Arch Rat. Mech. Anal. 12 pp 155– (1963)
[23] Werner, Arch. Rat. Mech. Anal. 18 pp 167– (1965)
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