Linear and nonlinear degenerate differential operators and applications

The boundary value and mixed value problems for linear and nonlinear singular degenerate abstract elliptic and parabolic equations are studied. The linear problems involve some parameters. The uniform Lp- separability properties of linear problems and the optimal regularity results for nonlinear problems are obtained. The equations include linear operators defined in Banach spaces, in which by choosing the spaces and operators we can obtain numerous classes of problems for singular degenerate differential equations which occur in a wide variety of physical systems.