In this Note we prove that the second Riemannian -Sobolev best constant depends continuously on g in the -topology when . The situation changes significantly in the case . In particular, we prove that is continuous on g in the -topology and is not in the -topology.
Dans cette Note nous prouvons que la deuxième meilleure constante dans l'inégalité de -Sobolev Riemannienne dépend continûment de g dans la topologie quand . La situation change radicalement lorsque . En particulier, nous montrons que est continu en g dans le -topologie et ne l'est pas dans le -topologie.
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@article{CRMATH_2007__345_10_579_0, author = {Barbosa, Ezequiel R. and Montenegro, Marcos}, title = {On the continuity of the second {Sobolev} best constant}, journal = {Comptes Rendus. Math\'ematique}, pages = {579--582}, publisher = {Elsevier}, volume = {345}, number = {10}, year = {2007}, doi = {10.1016/j.crma.2007.10.026}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.10.026/} }
TY - JOUR AU - Barbosa, Ezequiel R. AU - Montenegro, Marcos TI - On the continuity of the second Sobolev best constant JO - Comptes Rendus. Mathématique PY - 2007 SP - 579 EP - 582 VL - 345 IS - 10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.10.026/ DO - 10.1016/j.crma.2007.10.026 LA - en ID - CRMATH_2007__345_10_579_0 ER -
%0 Journal Article %A Barbosa, Ezequiel R. %A Montenegro, Marcos %T On the continuity of the second Sobolev best constant %J Comptes Rendus. Mathématique %D 2007 %P 579-582 %V 345 %N 10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.10.026/ %R 10.1016/j.crma.2007.10.026 %G en %F CRMATH_2007__345_10_579_0
Barbosa, Ezequiel R.; Montenegro, Marcos. On the continuity of the second Sobolev best constant. Comptes Rendus. Mathématique, Volume 345 (2007) no. 10, pp. 579-582. doi : 10.1016/j.crma.2007.10.026. http://archive.numdam.org/articles/10.1016/j.crma.2007.10.026/
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