2019
Том 71
№ 7

# 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

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

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.