Homotopical properties of a class of nonsmooth functions
type: Item
instance of: scholarly article
title: Homotopical properties of a class of nonsmooth functions
zbMATH Open document ID: 0722.58013
DOI: 10.1007/BF01766973
author: Marco Degiovanni
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1990-01-01T00:00:00Z
review text: The author develops an equivariant critical point theory for a class of (non-smooth) lower semicontinuous functionals defined on an open subset of a Hilbert space. This class of functionals f is given by the condition \[ (\alpha -\beta,u-v)\geq -\chi (u,v,f(u),f(v))(1+| \alpha |^ 2+| \beta |^ 2)| u-v|^ 2, \] for any \(\alpha \in \partial^-f(u)\), \(\beta \ni \partial^-f(v)\), where \(\chi\) is a continuous function and \(\partial^-f\) is the subdifferential of f. One of the main steps is the proof of the fact that the set \(D(f):=\{u; f(u)<\infty \}\) equipped with a suitable metric is an absolute neighborhood retract. The author also shows homotopical stability of sublevels of f under \(\Gamma\)-convergence.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 58E35
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 4190749
zbMATH Keywords: Lyusternik-Schnirelman category
zbMATH Keywords: equivariant critical point theory
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4190749