Sobolev inequalities with remainder terms.(English)Zbl 0577.46031
Le résultat principal concerne l’inégalité de Sobolev \[ \int_{\Omega}| \nabla u|^ 2\geq S_ n\| u\|^ 2_{2^*}+C(\Omega)[u]^ 2_{2^*/2}. \] Pour toute fonction \(u\in H^ 1_ 0(\Omega)\), où \(\Omega \subset {\mathbb{R}}^ n\) est un ouvert borné, \(S_ n\) est la meilleure constante de Sobolev dans \({\mathbb{R}}^ n\), \(2^*={\mathfrak n}/(n-2)\) et [ \(]_ p\) est la norme dans \(L^ p\) faible (espace de Marcinkiewicz).
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
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References:
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