Completeness theorems: Fichera's fundamental results and some new contributions

Abstract

After recalling Fichera’s fundamental results in the study of the problem of the completeness of particular solutions of a partial differential equation, we give some new completeness theorem. They concern the Dirichlet problem for a general elliptic operator of higher order with real constant coefficients in any number of variables.

Keywords

• Completeness theorems
• Higher order elliptic equations
• Potential theory