Some results on critical groups for a class of functionals defined on Sobolev Banach spaces

Cingolani, Silvia, and Vannella, Giuseppina. "Some results on critical groups for a class of functionals defined on Sobolev Banach spaces." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 12.4 (2001): 199-203. <http://eudml.org/doc/252307>.

@article{Cingolani2001,
abstract = {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.},
author = {Cingolani, Silvia, Vannella, Giuseppina},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {p-laplacian; Critical groups estimates; Morse index; -Laplacian; critical groups estimates},
language = {eng},
month = {12},
number = {4},
pages = {199-203},
publisher = {Accademia Nazionale dei Lincei},
title = {Some results on critical groups for a class of functionals defined on Sobolev Banach spaces},
url = {http://eudml.org/doc/252307},
volume = {12},
year = {2001},
}

TY - JOUR
AU - Cingolani, Silvia
AU - Vannella, Giuseppina
TI - Some results on critical groups for a class of functionals defined on Sobolev Banach spaces
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2001/12//
PB - Accademia Nazionale dei Lincei
VL - 12
IS - 4
SP - 199
EP - 203
AB - 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.
LA - eng
KW - p-laplacian; Critical groups estimates; Morse index; -Laplacian; critical groups estimates
UR - http://eudml.org/doc/252307
ER -