Soit Ω un ouvert borné et regulier dans , . On montre que l'inegalité de Hardy, liée à la distance au bord, avec meilleure constante (), peut être améliorée en ajoutant un multiple de la norme de Sobolev critique.
Let Ω be a smooth bounded domain in , . We show that Hardy's inequality involving the distance to the boundary, with best constant (), may still be improved by adding a multiple of the critical Sobolev norm.
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@article{CRMATH_2004__339_7_483_0, author = {Filippas, S. and Maz'ya, V.G. and Tertikas, A.}, title = {Sharp {Hardy{\textendash}Sobolev} inequalities}, journal = {Comptes Rendus. Math\'ematique}, pages = {483--486}, publisher = {Elsevier}, volume = {339}, number = {7}, year = {2004}, doi = {10.1016/j.crma.2004.07.023}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2004.07.023/} }
TY - JOUR AU - Filippas, S. AU - Maz'ya, V.G. AU - Tertikas, A. TI - Sharp Hardy–Sobolev inequalities JO - Comptes Rendus. Mathématique PY - 2004 SP - 483 EP - 486 VL - 339 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2004.07.023/ DO - 10.1016/j.crma.2004.07.023 LA - en ID - CRMATH_2004__339_7_483_0 ER -
%0 Journal Article %A Filippas, S. %A Maz'ya, V.G. %A Tertikas, A. %T Sharp Hardy–Sobolev inequalities %J Comptes Rendus. Mathématique %D 2004 %P 483-486 %V 339 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2004.07.023/ %R 10.1016/j.crma.2004.07.023 %G en %F CRMATH_2004__339_7_483_0
Filippas, S.; Maz'ya, V.G.; Tertikas, A. Sharp Hardy–Sobolev inequalities. Comptes Rendus. Mathématique, Tome 339 (2004) no. 7, pp. 483-486. doi : 10.1016/j.crma.2004.07.023. http://archive.numdam.org/articles/10.1016/j.crma.2004.07.023/
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