Carleman estimates and unique continuation property for the anisotropic differential-operator equations

Abstract

The unique continuation theorems for the anisotropic partial differential-operator equations with variable coefficients in Banach-valued L (p) -spaces are studied. To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations, the sufficient conditions are founded. By using these facts, the unique continuation properties are established. In the application part, the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.