Abstract
We establish a criterion for existence of an L 2-limit and a weak L 2-limit of a polyharmonic function on a regular analytic boundary of a bounded plane domain.
Similar content being viewed by others
References
Mikhalov V. P., “Existence of boundary values for biharmonic functions,” Mat. Sb., 195, No.12, 81–94 (2004).
Mikhailov V. P., “Existence of limit values of the solutions of a polyharmonic equation on the boundary of a domain,” Mat. Sb., 187, No.11, 89–114 (1996).
Mikhailov V. P., “Existence of boundary values for metaharmonic functions,” Mat. Sb., 190, No.10, 17–48 (1999).
Riesz F., “Uber die Randwerte eines Analytische Funktion,” Math. Z., Bd 18, 87–95 (1923).
Privalov I. I., Boundary Properties of Analytic Functions [in Russian], GITTL, Moscow (1950).
Mikhailov V. P., “On the boundary values of the solutions of elliptic equations in domains with smooth boundary,” Mat. Sb., 101, No.2, 163–188 (1976).
Vekua I. N., New Methods for Solving Elliptic Equations [in Russian], GITTL, Moscow; Leningrad (1948).
Author information
Authors and Affiliations
Additional information
Original Russian Text Copyright © 2005 Mikhailov V. P.
The author was supported by the Russian Foundation for Basic Research (Grant 01-01-00988) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1542.2003.1).
In memory of Tadei Ivanovich Zelenyak.
__________
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 1125–1137, September– October, 2005.
Rights and permissions
About this article
Cite this article
Mikhailov, V.P. Existence of the Boundary Value of a Polyharmonic Function. Sib Math J 46, 902–912 (2005). https://doi.org/10.1007/s11202-005-0087-x
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11202-005-0087-x