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Abstract: This paper treats some variational principles for solutions of inhomogeneous p-Laplacian boundary value problems on exterior regions with dimension . Existence-uniqueness results when are provided in a space of functions that contains . Functions in 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 -imbedding theorem. Also an existence result for a general variational problem of this type is obtained. [Copyright &y& Elsevier]

Abstract: This paper describes spectral representations and approximations of solutions of second order, self-adjoint, linear elliptic boundary value problems on exterior regions in , for . Inhomogeneous Dirichlet, Robin and Neumann boundary conditions are treated. Some new trace results are proved and used to provide spectral characterizations of the boundary traces of functions in . Orthonormal bases of these Hilbert spaces are derived using a theory of Steklov eigenproblems. The Steklov eigenfunctions of a regularized Laplace operator on the exterior of a ball are explicitly determined when . [Copyright &y& Elsevier]