Separable anisotropic elliptic operators and applications

This paper focuses on boundary value problems for anisotropic differential-operator equations of high order with variable coefficients in the half plane. Several conditions are obtained which guarantee the maximal regularity of anisotropic elliptic and parabolic problems in Banach-valued L _p -spaces. Especially, it is shown that this differential operator is R-positive and is a generator of an analytic semigroup. These results are also applied to infinite systems of anisotropic type partial differential equations in the half plane.