2019
Том 71
№ 11

# Estimates of generalized solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a domain with conical boundary point

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 $$\frac{d}{{dx_i }}a_i (x,u,u_x ) + a(x,u,u_x ) = 0,x \in G,$$ 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.

English version (Springer): Ukrainian Mathematical Journal 50 (1998), no. 10, pp 1483-1495.

Citation Example: 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. Mat. Zh. - 1998. - 50, № 10. - pp. 1299–1309.

Full text