Runge property and approximation by complete systems of solutions for strongly elliptic equations

Abstract

We give an overview of some concepts related to the approximation of solutions of a strongly elliptic operator. A definition of a complete system of classical solutions is given, and we show how using the Runge property, it is possible to extend the completeness of these systems onto strictly internal domains in the , and norms. This result is applied to Schrödinger equations with potentials possessing some symmetries.