Abstract
In May 1978 Professor A. V. Balakrishnan invited me to report about boundary values of the solutions of elliptic equations in his seminar at the University of California, at UCLA. I thank him for this invitation. The present article is a summary of my report.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Fatou, Séries trigonometriques et séries de Taylor. Acta Math., 30, 335–400, (1906).
F. Riesz, Über die Randwerte einer analytischen Funktion. Math. Zs., 18, 87–95, (1923).
R. Nevanlinna, Über die Anwendung des Poissonshen Integrals zur Untersuchung der Singularitäten analytischer Funktion. Verh. des 5 Math. Congress, Helsingfors, 273–289, (1923).
I. I. Privalov, The boundary problems and classes of harmonic and subharmonic functions in arbitrary domains. Math. Sbornik, 6, 345–376, (1939).
N. N. Lusin, Sur une propriété des fonctions à carré Sommable. Bull. Calcutta Math. Soc., 20, 139–154, (1930).
L. Calderon, On the behaviour of harmonic functions on the boundary. Trans. Amer. Math. Soc., 68, 47–54, (1950).
E. M. Stein, Singular integrals and differentiability properties of functions. Princeton Univ. Press., 1970.
I. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series. Proc. Lond. Math. Soc., 42, 52–89, (1936).
V. P. Mikhailov, On the boundary values of solutions of elliptic equations in domains with a smooth boundary. Math. Sbornik, 101, 143–166, (1976).
G. Cimmino, Nuovo tipo di condizione al cóntoruo 1 nuovo metodo di trattazione pre il problema generalizzato di Dirichlet. Rend. Circ. Mat. Palermo, 61, 177–221, (1938).
J. Necas, On the solutions of elliptic partial differential equations of the second order with inbounded Dirichlet's integral. Math. Journ. of Chekhoslovakija, 10, 283–298, (1960).
V. P. Mikhailov, On the Dirichlet's problem for elliptic equation of the second order. Diff. equations, XII, 1877–1891, (1976).
A. K. Guscin and V. P. Mikhailov, On the behaviour near the boundary of the solution of third boundary-value problem for elliptic equation of the second order. Complex analysis and its applications, “Nauka” Moscow, 193–202, 1978.
Author information
Authors and Affiliations
Additional information
Communicated by A. V. Balakrishnan
Rights and permissions
About this article
Cite this article
Mikhailov, V.P. On the boundary values of the solutions of elliptic equations. Appl Math Optim 6, 193–199 (1980). https://doi.org/10.1007/BF01442894
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01442894