Separable properties of differential operators in exterior regions and applications

Abstract

The abstract elliptic and parabolic equations on exterior regions are considered. The equations have top-order variable coefficients. The separability properties of boundary value problems for elliptic equation and well-posedness of the Cauchy problem for parabolic equations are established. We obtain the maximal regularity properties of a wide class of elliptic and parabolic equations by choosing the space E and the operator A which appear in the field of physics. In application, the maximal regularity properties of Cauchy problem for anisotropic parabolic equations and system of parabolic equations are derived