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Compactness of Orlicz-Sobolev space imbeddings for unbounded domains Cahill, Ian Graham

Abstract

In this thesis we are concerned with the compactness of im-beddings, for unbounded domains, of Orlicz-Sobolev spaces. Donaldson and Trudinger [6] have given a generalization of the Sobolev imbedding theorem and the Rellich-Kondrachov compactness theorem for Sobolev spaces to the case of Orlicz-Sobolev spaces on bounded domains. Clark, Adams, and Fournier [1], [2], [3], and [5] have given extensions of the Sobolev compactness results to certain unbounded domains. In this thesis we consider similar extensions for Orlicz-Sobolev spaces.

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