The Rellich-Kondrachov theorem for unbounded domains.

The full Kondrachov compactness theorem for Sobolev imbeddings of the type W (G)→ W (G) on bounded domains G in Ris extended to a large class of unbounded domains with 'reasonable' n- 1 dimensional boundaries. A Poincaré inequality is obtained for such domains and a compactness theorem for traces of functions in W (G) on lower dimensional hyperplanes is also proved. [ABSTRACT FROM AUTHOR]