Optimal Orlicz-Sobolev embeddings
Cianchi, Andrea
Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, p. 427-474 / Harvested from Project Euclid
An embedding theorem for the Orlicz-Sobolev space $W^{1,A}_{0}(G)$, $G\subset \mathbb{R}^n$, into a space of Orlicz-Lorentz type is established for any given Young function $A$. Such a space is shown to be the best possible among all rearrangement invariant spaces. A version of the theorem for anisotropic spaces is also exhibited. In particular, our results recover and provide a unified framework for various well-known Sobolev type embeddings, including the classical inequalities for the standard Sobolev space $W^{1,p}_{0}(G)$ by O'Neil and by Peetre ($1\leq p< n$), and by Brezis-Wainger and by Hansson ($p=n$).
Publié le : 2004-06-14
Classification:  Sobolev inequalities,  Orlicz spaces,  rearrangement invariant spaces,  interpolation,  46E35,  46E30
@article{1087482022,
     author = {Cianchi, Andrea},
     title = {Optimal Orlicz-Sobolev embeddings},
     journal = {Rev. Mat. Iberoamericana},
     volume = {20},
     number = {1},
     year = {2004},
     pages = { 427-474},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087482022}
}
Cianchi, Andrea. Optimal Orlicz-Sobolev embeddings. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp.  427-474. http://gdmltest.u-ga.fr/item/1087482022/