Pukalsky I. Boundary problems for irregularly parabolic and elliptic equations with degeneration and peculiarities

. Dissertation deals with the construction of correct solv-ability classes of the basic boundary problems for parabolic and elliptic equations with degeneration and peculiarities. Parabolic equations of second order with power pecu-liarities of an arbitrary order with respect to time variable at fixed moment and with nonlocal conditions and arbitrary space variables in some quantity of point inside a domain or on a collateral line are considered. Correct solvability of the first boundary problem, the boundary problem with in-clined derivative, the one-side boundary problem and the nonlocal Cauchy's problem have been ascertained. Correct solvability of the Dirichlet's problem, the prob-lem with inclined derivative and the one-side boundary problem for the elliptic equations of the second order with power peculiarities of an arbitrary order with respect to any variables on a boundary line or inside a domain have been ascertained. Correct solvability classes of Cauchy's problem and boundary problem for parabolic equations of 2b-order (b > 1) with power peculiarities of arbitrary order with respect to time variable in fixed point of a domain or on a boundary line of domain have been formed. The results of investigation are applied to optimal con-trol control problem in cases of internal, boundary and final control.