Hostname: page-component-5c6d5d7d68-vt8vv Total loading time: 0.001 Render date: 2024-08-22T19:11:12.288Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Dirichlet–Neumann–Third mixed boundary value problem for the Helmholtz equation

Published online by Cambridge University Press:  14 November 2011

M. David
M. David
Affiliation:
Scientific Department of the Ministry of Defense, P.O. Box 2250, Israel
Get access Rights & Permissions [Opens in a new window]

Synopsis

Existence and uniqueness theorems are proved for the solution of a Dirichlet-Neumann-Third mixed boundary value problem for the Helmholtz equation in ℝ3. The proofs make use of an equivalent system of two integral equations of the second kind.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 3-4 , 1983 , pp. 221 - 233
Copyright
Copyright © Royal Society of Edinburgh 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Gunter, N. M.. La theorie du potentiel et ses applications aux problemes fondamentaux de la physique mathematique (Paris: Gauthier-Villars, 1934).Google Scholar
2.Kress, R. and Roach, G. F.. On mixed boundary value problems for the Helmholtz equation. Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 65–77.CrossRefGoogle Scholar
3.Leis, R.. Zur Dirichletschen Randwertaufgabe des Außenraumes der Schwingangsgleichung. Math. Z. 90 (1965), 205–211.CrossRefGoogle Scholar
4.Netuka, I.. An operator connected with the Third boundary value problem in potential theory. Czechoslovak Math. J. 22 (97) (1972), 462–489.CrossRefGoogle Scholar
5.Zabreyko, P. P., Koshelev, A. I., Krasnoselskii, M. A., Mikhlin, S. G., Rakovshchik, L. S. and Stetsenko, V. Ya.. Integral Equations—a reference text (Moskow, 1968) (Leyden: Nordhoff).Google Scholar