Abstract
In the present paper the sufficient condition for existence of the mean square limit of a biharmonic function in a ball is established.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. P. Mikhailov, “On the boundary values of solutions of elliptic equations in domains with a smooth boundary,” Math. USSR-Sbornik 30(2), 143–166 (1976).
J. E. Littlewood and R. Paley, “Theorems on Fourier series and power series (II),” Proc. Lond. Math. Soc. 42(1), 52–89 (1936).
J. E. Littlewood and R. Paley, “Theorems on Fourier series and power series(III),” Proc. Lond. Math. Soc. 43, 105–126 (1937).
Ya. A. Roitberg, “The limit values, along surfaces parallel to the boundary, of the generalized solutions of elliptic equations,” Doklady USSR Acad. Sciences 238(6), 1303–1306 (1978) [in Russian].
V. P. Mikhailov, “Existence of boundary values for metaharmonic functions,” Sbornik: Mathematics 190(10), 1417–1448 (1999).
V. P. Mikhailov, Proc. Int.Workshop “Differential Equations and Their Applications” (Samara, 1998).
V. P. Mikhailov, “A sufficient condition for the existence of limit values of solutions of an elliptic equation on the boundary,” Theor. Math. Phys. 157(3), 1733–1744 (2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
The text was submitted by the author in English.
Rights and permissions
About this article
Cite this article
Mikhailov, V.P. On Existence of a boundary value of a biharmonic function in a ball. P-Adic Num Ultrametr Anal Appl 4, 34–45 (2012). https://doi.org/10.1134/S2070046612010050
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2070046612010050