Entartete lineare elliptische Differentialgleichungen und anisotrope Sobolewräume: Existenz schwacher Lösungen

Abstract

This paper deals with Dirichiet boundary value problems for degenerated linear elliptic systems in bounded domains. Generalising the condition of strong ellipticity we extend the theory of weak solutions to a class of certain systems. In these ones the highest derivatives with respect to several variables or to several unknowns have different orders. For such system Gårding’s inequality in anisotropic Sobolov spaces can be proved. In this way we get existence and uniqueness results for weak solutions.