2019
Том 71
№ 8

All Issues

Plesha M. I.

Articles: 2
Brief Communications (Ukrainian)

Unimprovable Integral Estimate for Solutions of the Dirichlet Problem for Quasilinear Elliptic Equations of the Second Order in a Neighborhood of an Edge

Plesha M. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 6. - pp. 860-865

We obtain an exact estimate for the second derivatives of solutions (in the weight Sobolev norm) of the Dirichlet problem for quasilinear second-order elliptic equations of nondivergence type in a neighborhood of an edge of a domain.

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.