Superposition of imbeddings and Fefferman's inequality

Krbec, Miroslav ; Schott, Thomas

Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999), p. 629-637 / Harvested from Biblioteca Digitale Italiana di Matematica

Résumé

In questo lavoro si studiano condizioni sufficienti sulla funzione peso $V$, espresse in termini di integrabilità, per la validità della disuguaglianza $$ \left( \int_{B} u^{2}(x) V(x) \, dx \right)^{\frac{1}{2}}\leq c \left(\int_{B} (\nabla u(x))^{2} \, dx \right)^{\frac{1}{2}}, $$ dove $B$ denota una sfera in $\mathbb{R}^{N}$. Usando una tecnica di decomposizione di immersioni si dimostrano condizioni sufficienti in termini di appartenenza a spazi di Lebesgue, Lorentz-Orlicz e/o di tipo debole. Come applicazioni vengono fornite condizioni sufficienti per la proprietà forte di prolungamento unico per $|\Delta u|\leq V|u|$ nelle dimensioni 2 e 3.

Détail

Publié le : 1999-10-01

MR 1719550 | Zbl 0948.46023

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