Volume 45, № 11, 1993
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1467–1475
The direct theorem of the theory of approximation of harmonic functions is established in the case of functions defined on a compact set, the complement of which with respect to ? is a John domain.
Boundary-value problems for an elliptic equation with complex coefficients and a certain moment problem
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1476–1483
Elliptic systems of two second-order equations, which can be written as a single equation with complex coefficients and a homogeneous operator, are studied. The necessary and sufficient conditions for the connection of traces of a solution are obtained for an arbitrary bounded domain with a smooth boundary. These conditions are formulated in the form of a certain moment problem on the boundary of a domain; they are applied to the study of boundary-value problems. In particular, it is shown that the Dirichlet problem and the Neumann problem are solvable only together. In the case where the domain is a disk, the indicated moment problem is solved together with the Dirichlet problem and the Neumann problem. The third boundary-value problem in a disk is also investigated.
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1484–1494
We develop Kufarev's method for determining unknown parameters in the Schwarz-Christoffel integral in the case of conformal mapping of polygonal regions with boundary normalization.
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1495–1502
For traces of generalized solutions of elliptic systems on smooth manifolds, we study the dependence of the Hausdorff dimension of the set of points at which a solution is not smooth on the modulus of ellipticity of a system.
Averaging of Neumann problems for nonlinear elliptic equations in regions of framework type with thin channels
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1503–1513
TheG-convergence of operators of the Neumann problem is established in regions with framework-type periodic structure with thin channels. A representation of the coefficients of aG-limiting operator is obtained.
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1514–1521
We prove the general limit theorem on probability of large deviations of the logarithm of the likelihood ratio with the null hypothesis and alternative. Weaker versions of the principle of large deviations are obtained in predictable terms for the problem of distinguishing the counting processes. The case of counting processes with deterministic compensators is studied.
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1522–1533
Upper and lower bounds are established for the rate of rational approximation of functions piecewise analytic on tangent continua. In some special cases, these bounds are coordinated depending on the mutual location of the continua.
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1534–1541
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1542–1566
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1567–1570
We study the properties of solutions of weakly nonlinear parabolic equations in cylindrical domains. The existence conditions are established for local nontangential limits as t ? 0.
Qualitative properties of solutions of the Neumann problem for a higher-order quasilinear parabolic equation
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1571–1579
The property of localization of perturbations is proved for a solution of an initial boundary-value Neumann problem in a regionD=?x, t>0, where ? is a region in Rnwith a noncompact boundary.
Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1580–1584