Abstract
We obtain a priori estimates for generalized second derivatives (in the Sobolev weighted norm) of solutions of the Dirichlet problem for the elliptic equation
in the neighborhood of a conical boundary point of the domain G. We give an example that demonstrates that the estimates obtained are almost exact.
Similar content being viewed by others
References
M. V. Borsuk, “Behavior of generalized solutions of the Dirichlet problem for quasilinear elliptic divergent equations of the second order near a conical point,” Sib. Mat. Zh., 31, No. 6, 25–38 (1990).
M. V. Borsuk, “Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in the domain with conical boundary point,” Differents. Uravn., 31, No. 6, 1001–1007 (1995).
P. Tolksdorf, “On the Dirichlet problem for quasilinear equations with conical boundary points,” Commun. Part. Differen. Equat., 8, No. 7, 773–817 (1983).
O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1973).
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of the Second Order [Russian translation], Nauka, Moscow (1989).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1299–1309, October, 1998.
Rights and permissions
About this article
Cite this article
Borsuk, M.V., Plesha, M.I. Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point. Ukr Math J 50, 1483–1495 (1998). https://doi.org/10.1007/BF02513489
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02513489