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⊊RNU⊊RN with dimension N⩾3N⩾3. Existence-uniqueness results when p∈(1,N)p∈(1,N) are provided in a space E1,p(U)E1,p(U) of functions that contains W1,p(U)W1,p(U). Functions in E1,p(U)E1,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 LpLp-imbedding theorem. Also an existence result for a general variational problem of this type is obtained.