Entartete lineare elliptische Differentialgleichungen und anisotrope Sobolewräume: Existenz schwacher Lösungen. (Degenerated linear elliptic differential equations and anisotropic Sobolev spaces: existence of weak solutions) (Q1092325)

The author treats Dirichlet boundary value problems in bounded domains. The highest derivatives with respect to several variables or unknowns have different orders. This leads into unisotropic Sobolev spaces. For such problems the concept of ellipticity is generalized, and a Gårdings inequality is proved. Thus existence and uniqueness for weak solutions is achieved. A proof of regularity is announced.