Topology of sobolev mappings, II

This paper addresses some topological and analytical issues concern- ing Sobolev mappings between compact Riemannian manifolds. Among the results we obtained are unified proofs of various generalizations of results obtained in a recent work of Brezis and Li. In particular we solved two conjectures in (BL). We also give a topological obstruction for the weak sequential density of smooth maps in a given Sobolev mapping space. Finally we show a necessary and suf- ficient topological condition under which the smooth maps are strongly dense in the Sobolev spaces. The earlier result, Theorem 1 of (B2), was shown to be not correct.

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