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The problem of optimal control of the system described by the oblique derivative problem forthe elliptic equation of the second order is studied. Cases of internal and boundary managementare considered. The quality criterion is given by the sum of volume and surface integrals.The coefficients of the equation and the boundary condition allow power singularities of arbitraryorder in any variables at some set of points. Solutions of auxiliary problems with smooth coefficients are studied to solve the given problem. Using a priori estimates, inequalities are established for solving problems and their derivatives in special H\"{o}lder spaces. Using the theorems of Archel and Riess, a convergent sequence is distinguished from a compact sequence of solutions to auxiliary problems, the limiting value of which will bethe solution to the given problem. The necessary and sufficient conditions for the existence of the optimal solution of the systemdescribed by the boundary value problem for the elliptic equation with degeneracy have been established.

For a second-order parabolic equation, we consider a one-sided boundary-value problem with impulsive conditions with respect to the time variable. The coefficients of equation and the boundary conditions have power singularities of any order in time and space variables on a certain set of points. We also establish conditions for the existence and uniqueness of solution to the posed problem in Holder spaces with power weights.

For a second-order parabolic equation, we consider a multipoint (in time) problem with oblique derivative. The coefficients of the equation and boundary condition have power singularities of any order in time and spatial variables on a certain set of points. We establish conditions for the existence and uniqueness of solution of the posed problem in Holder’s spaces with power weight.

For a second-order parabolic equation, we consider a problem with oblique derivative and impulsive action. The coefficients of the equation and the boundary condition have power singularities of any order in the time and space variables on a certain set of points. We establish conditions for the existence and uniqueness of the solution of the posed problem in Holder spaces with power weight.