Optimal embeddings of Sobolev type spaces into spaces of continuous functions are established. On extending the classical Morrey embedding on the Hoelder continuity of functions with weak derivatives in suitable Lebesgue spaces, our results provide the sharp modulus of continuity of functions whose weak derivatives of a given order belong to a more general rearrangement invariant space. In particular, embeddings of Orlicz-Sobolev spaces into spaces of continuous functions are characterized.

On the modulus of continuity of weakly differentiable functions / Cianchi, Andrea; Monia, Randolfi. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 60:(2011), pp. 1939-1973.

On the modulus of continuity of weakly differentiable functions

CIANCHI, ANDREA;
2011

Abstract

Optimal embeddings of Sobolev type spaces into spaces of continuous functions are established. On extending the classical Morrey embedding on the Hoelder continuity of functions with weak derivatives in suitable Lebesgue spaces, our results provide the sharp modulus of continuity of functions whose weak derivatives of a given order belong to a more general rearrangement invariant space. In particular, embeddings of Orlicz-Sobolev spaces into spaces of continuous functions are characterized.
2011
60
1939
1973
Cianchi, Andrea; Monia, Randolfi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/787555
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