$L^2$-estimates for the $d$-equation and Witten’s proof of the Morse inequalities

Bo Berndtsson

Displaying similar documents to “ $L^{2}$ -estimates for the $d$ -equation and Witten’s proof of the Morse inequalities”

Morse theory indomitable

Raoul Bott (1988)

Publications Mathématiques de l'IHÉS

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

Silvia Cingolani, Giuseppina Vannella (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We present critical groups estimates for a functional $f$ defined on the Banach space $W_{0}^{1, p} (Ω)$ , $Ω$ bounded domain in $R^{N}$ , $2 < p < \infty$ , 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.