Evolution problems and minimizing movements
type: Item
instance of: scholarly article
title: Evolution problems and minimizing movements
zbMATH Open document ID: 0835.49021
author: Ugo Gianazza
author: Massimo Gobbino
author: Giuseppe Savaré
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1995-07-25T00:00:00Z
full work available at URL: https://eudml.org/doc/244234
review text: In the paper E. De Giorgi's ideas of MM (``minimizing movements'') and of GMM (``generalized minimizing movements'') are developed in two directions. First, in connection with ODE's, various problems concerning the interrelations between the MM, GMM and the solution sets to the Cauchy problem for gradient type differential equations are considered. Also in this part, the authors present some generalization to the case of arbitrary metric spaces of the theory of maximal slope curves developed in Hilbert spaces by E. De Giorgi, A. Marino, M. Tosques, M. Degiovanni, C. Saccon,\dots. Second, in the domain of PDE's the authors present an unified framework for formulating and solving some recent conjectures of De Giorgi concerning the parabolic equations and minimizing movements in Hilbert or in uniformly convex Banach spaces. Some open problems, concerning for instance the regularity or semigroup property, for MM or GMM are also formulated.
Mathematics Subject Classification ID: 90C99
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 766465
zbMATH Keywords: variational evolution problems
zbMATH Keywords: Cauchy problem
zbMATH Keywords: gradient type differential equations
zbMATH Keywords: maximal slope curves
zbMATH Keywords: parabolic equations
zbMATH Keywords: minimizing movements
reviewed by: Zdzisław Denkowski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 766465