Sunto
Si considera l'equazione variazionale in R n
dove 0<λ 0⩽a(x)⩽Λ 0<∞e F è una funzione crescente, convessa e tale che pF(t) ⩽⩽tF′(t)⩽qF(t) (1<p⩽q<∞). Si dimostra che le soluzioni molto deboli di tale equazione che appartengono ad un opportuno spazio di Orlicz-Sobolev, sono nulle quasi ovunque.
Abstract
Let us consider the variational equation in R n
where 0<λ0⩽a(x)⩽Λ0<∞ and F is a convex increasing function such that pF(t) ⩽⩽tF′ (t)⩽qF(t) where 1<p⩽q<∞. We prove that the very weak solutions of such equation, belonging to a suitable Orlicz-Sobolev space, must be zero almost everywhere.
Résumé
Dans cet article on considère l'équation variationelle in R n
où 0<λ 0⩽a(x)⩽Λ0 <∞ et F est une fonction convexe, croissante, telle que pF(t) ⩽⩽tF′ (t)⩽qF(t) où 1<p⩽q<∞. On montre que les solutions très faibles de cette équation, qui sont dans un particulier espace de Orlicz-Sobolev, sont zero presque partout.
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This work has been performed as a part of a National Research Project supported by M.U.R.S.T.