SEPARABILITY PROPERTIES OF SINGULAR DEGENERATE ABSTRACT DIFFERENTIAL OPERATORS AND APPLICATIONS

Abstract

We study separability and spectral properties of singular degenerate elliptic equations in vector-valued L-p spaces. We prove that a realization operator according to this equation with some boundary conditions is separable and Fredholm in L-p. The leading part of the associated differential operator is not self-adjoint. The sharp estimate of the resolvent, discreteness of spectrum and completeness of root elements of this operator is obtained. Moreover, we show that this operator is positive and generates a holomorphic C-0-semigroups on L-p. In application, we examine the regularity properties of nonlocal boundary value problem for degenerate elliptic equation and for the system of degenerate elliptic equations of either finite or infinite number.