Abstract
We obtain the exact estimates of the rate of decrease and some estimates for the modulus of the gradient of the solution in a neighborhood of a conical point of the boundary.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Maz’ya V. G., Sobolev Spaces [in Russian], Nauka, Moscow (1987).
Ladyzhenskaya O. A. and Ural’tseva N. N., Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1973).
Gilbarg D. and Trudinger N. S., Elliptic Partial Differential Equations of Second Order [Russian translation], Nauka, Moscow (1989).
Miersemann E., “Zur Regularitaet verallgemeinerter Losungen von quasilinearen elliptischen Differentialgleichungen zweiter Ordnung in Gebieten mit Ecken mit Ecken,” Z. Anal. Anwendungen, Bd 1, No.4, 59–71 (1982).
Toreadors P., “On quasilinear boundary value problems in domains with corners,” Nonlinear Anal., 5, No.7, 721–735 (1981).
Borsuk M. V., “The behavior of generalized solutions of the Dirichlet problem for the second-order quasilinear elliptic divergence type equations near a conical point,” Sibirsk. Mat. Zh., 31, No.6, 25–38 (1990).
Kondrat’ev V. A. and Ole \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) nik O. A., “Boundary value problems for partial differential equations in nonsmooth domains,” Uspekhi Mat. Nauk, 38, No.2, 4–76 (1983).
Gadjiev T. S., “On behavior of solutions and their derivatives in domains with angular points for quasilinear equations,” Izv. Akad. Nauk AzSSR Ser. Fiz.-Tekh. Mat. Nauk, 10, No.2–3, 27–32 (1989).
Gadjiev T. S., “On solutions to mixed boundary value problems for second-order quasilinear elliptic equations in arbitrary bounded domains,” in: Mathematical Physics and Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev, 1986, No. 5, pp. 56–59.
Toreadors P., “On the Dirichlet problem for quasilinear equations in domains with conical boundary points,” Comm. Partial Differential Equations, 8, No.7, 773–817 (1983).
Filippov A. F., “Smoothness of weak solutions near the vertex of a polyhedral angle,” Differentsial’nye Uravneniya, 9, No.10, 1889–1903 (1973).
Lieberman G. M., “Boundary regularity for solutions of degenerate elliptic equations,” Nonlinear Anal. Methods Appl., 12, No.11, 1203–1219 (1988).
Author information
Authors and Affiliations
Additional information
Original Russian Text Copyright © 2005 Gadjiev T. S.
Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Zhurnal, Vol. 46, No. 2, pp. 325–331, March–April, 2005.
Rights and permissions
About this article
Cite this article
Gadjiev, T.S. Some exact estimates of weak solutions to a mixed boundary value problem for nonlinear equations in domains with nonsmooth boundary. Sib Math J 46, 254–259 (2005). https://doi.org/10.1007/s11202-005-0025-y
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11202-005-0025-y