Separable differential operators and applications

The nonlocal boundary value problems for degenerate differential-operator equations with variable coefficients are studied. The $L_p$ separability properties of elliptic problems and well-posedeness of parabolic problems in mixed $L_\mathbf p$ spaces are derived. Then by using the regularity properties of linear problems, the existence and uniqueness of solution of nonlinear elliptic problem is obtained. Note that applications of these problems can be models of different physics process.