2019
Том 71
№ 10

All Issues

Borsuk M. V.

Articles: 2
Article (Ukrainian)

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

Borsuk M. V., Plesha M. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 10. - pp. 1299–1309

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.

Article (Ukrainian)

On the solvability of the dirichlet problem for elliptic nondivergent equations of the second order in a domain with conical point

Borsuk M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 1. - pp. 13-24

We study the problem of solvability of the Dirichlet problem for second-order linear and quasilinear uniformly elliptic equations in a bounded domain whose boundary contains a conical point. We prove new theorems on the unique solvability of a linear problem under minimal smoothness conditions for the coefficients, right-hand sides, and the boundary of the domain. We find classes of solvability of the problem for quasilinear equations under natural conditions.