p-Laplacian boundary value problems on exterior regions

This paper treats some variational principles for solutions of inhomogeneous p-Laplacian boundary value problems on exterior regions U ⊊ R N with dimension N ⩾ 3 . Existence-uniqueness results when p ∈ ( 1 , N ) are provided in a space E 1 , p ( U ) of functions that contains W 1 , p ( U ) . Functions in E 1 , p ( U ) are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an L p -imbedding theorem. Also an existence result for a general variational problem of this type is obtained.