no. 2
Optimal limiting embeddings for Δ-reduced Sobolev spaces in L 1
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 2, pp. 217-230.

We prove sharp embedding inequalities for certain reduced Sobolev spaces that arise naturally in the context of Dirichlet problems with L 1 data. We also find the optimal target spaces for such embeddings, which in dimension 2 could be considered as limiting cases of the Hansson–Brezis–Wainger spaces, for the optimal embeddings of borderline Sobolev spaces W 0 k,n/k .

@article{AIHPC_2014__31_2_217_0,
     author = {Fontana, Luigi and Morpurgo, Carlo},
     title = {Optimal limiting embeddings for {\ensuremath{\Delta}-reduced} {Sobolev} spaces in $ {L}^{1}$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {217--230},
     publisher = {Elsevier},
     volume = {31},
     number = {2},
     year = {2014},
     doi = {10.1016/j.anihpc.2013.02.007},
     mrnumber = {3181666},
     zbl = {1316.46035},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.02.007/}
}
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Fontana, Luigi; Morpurgo, Carlo. Optimal limiting embeddings for Δ-reduced Sobolev spaces in $ {L}^{1}$. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 2, pp. 217-230. doi : 10.1016/j.anihpc.2013.02.007. http://www.numdam.org/articles/10.1016/j.anihpc.2013.02.007/

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