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Abstract and Applied Analysis
Volume 2005, Issue 4, Pages 437-448
http://dx.doi.org/10.1155/AAA.2005.437

The sobolev embeddings are usually sharp

A. Fraysse and S. Jaffard

Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris XII Val de Marne, 61 avenue du Général de Gaulle, Créteil Cedex 94010, France

Received 10 November 2003

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let x0∈ℝd; we study the Hölder regularity at x0 of a generic function of the Sobolev space Lp,s(ℝd) and of the Besov space Bps,q(ℝd) for s−d/p>0. The setting for genericity is supplied here by HP-residual sets.