Linear and nonlinear abstract elliptic equations with <i>VMO</i> coefficients and applications

Abstract

In this paper, maximal regularity properties for linear and nonlinear elliptic differential-operator equations with VMO (vanishing mean oscillation) coefficients are studied. For linear case, the uniform separability properties for parameter dependent boundary value problems is obtained in spaces. Then the existence and uniqueness of a strong solution of the boundary value problem for a nonlinear equation is established. In application, the maximal regularity properties of the anisotropic elliptic equation and the system of equations with VMO coefficients are derived. MSC: 58I10, 58I20, 35Bxx, 35Dxx, 47Hxx, 47Dxx.