Geodesic
Some results on critical groups for a class of functionals defined on Sobolev Banach spaces
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 12 (2001) no. 4, pp. 199-203.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We present critical groups estimates for a functional $f$ defined on the Banach space $W^{1,p}_{0}(\Omega)$, $\Omega$ bounded domain in $\mathbb{R}^{N}$, $2 p \infty$, associated to a quasilinear elliptic equation involving $p$-laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of $f$ in each critical point, we compute the critical groups of $f$ in each isolated critical point via Morse index.
Presentiamo stime di gruppi critici per un funzionale $f$ definito sullo spazio di Banach $W^{1,p}_{0}(\Omega)$, $\Omega$ dominio limitato in $\mathbb{R}^{N}$, $2 p \infty$, associato a una equazione ellittica che coinvolge il $p$-laplaciano. Nonostante la mancanza di una struttura di Hilbert e di proprietà di Fredholm del differenziale secondo di $f$ nei punti critici, valutiamo i gruppi critici di $f$ in ogni punto critico isolato mediante l’indice di Morse. 
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     title = {Some results on critical groups for a class of functionals defined on {Sobolev} {Banach} spaces},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
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Cingolani, Silvia; Vannella, Giuseppina. Some results on critical groups for a class of functionals defined on Sobolev Banach spaces. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 12 (2001) no. 4, pp. 199-203. http://geodesic.mathdoc.fr/item/RLIN_2001_9_12_4_a0/

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