Optimal limiting embeddings for Δ-reduced Sobolev spaces in
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 2, pp. 217-230
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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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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 -
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%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://geodesic.mathdoc.fr/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, Tome 31 (2014) no. 2, pp. 217-230. doi: 10.1016/j.anihpc.2013.02.007
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