We prove sharp embedding inequalities for certain reduced Sobolev spaces that arise naturally in the context of Dirichlet problems with 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 .
@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/} }
TY - JOUR AU - Fontana, Luigi AU - Morpurgo, Carlo TI - Optimal limiting embeddings for Δ-reduced Sobolev spaces in $ {L}^{1}$ JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 217 EP - 230 VL - 31 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.02.007/ DO - 10.1016/j.anihpc.2013.02.007 LA - en ID - AIHPC_2014__31_2_217_0 ER -
%0 Journal Article %A Fontana, Luigi %A Morpurgo, Carlo %T Optimal limiting embeddings for Δ-reduced Sobolev spaces in $ {L}^{1}$ %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 217-230 %V 31 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.02.007/ %R 10.1016/j.anihpc.2013.02.007 %G en %F AIHPC_2014__31_2_217_0
Fontana, Luigi; Morpurgo, Carlo. Optimal limiting embeddings for Δ-reduced Sobolev spaces in $ {L}^{1}$. Annales de l'I.H.P. Analyse non linéaire, Volume 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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