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. 
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     author = {Cingolani, Silvia and Vannella, Giuseppina},
     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},
     pages = {199--203},
     publisher = {mathdoc},
     volume = {Ser. 9, 12},
     number = {4},
     year = {2001},
     zbl = {1072.58005},
     mrnumber = {MR1898461},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2001_9_12_4_a0/}
}
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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/