Abstract
The modulus of continuity of the solution to the Dirichlet problem is investigated for a second-order parabolic equation at a regular boundary point. A bound for the modulus of continuity is obtained in terms of the capacity. The coefficients of the equation are required to satisfy a Dini condition (uniformly).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
E. M. Landis, “S-capacity and its application to the study of solutions of second-order elliptic equations with discontinuous coefficients,” Matem. Sb.,76(118), No. 4, 186–213 (1969).
V. G. Maz'ya, “Modulus of continuity of the solution for the Dirichlet problem near an irregular boundary,” in: Problems of Mathematical Analysis [in Russian], Leningrad (1966), pp. 45–58.
A. A. Novruzov, “On the modulus of continuity of the solution to the Dirichlet problem at a regular boundary point,” Matem. Zametki,12, No. 1, 67–72 (1972).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 587–593, April, 1976.
Rights and permissions
About this article
Cite this article
Novruzov, A.A. Modulus of continuity of the solution to the Dirichlet problem for a second-order parabolic equation. Mathematical Notes of the Academy of Sciences of the USSR 19, 356–359 (1976). https://doi.org/10.1007/BF01156797
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01156797