Local Minimization, Variational Evolution and [Gamma]-Convergenc
General Material Designation
[Book]
Other Title Information
:[delta
First Statement of Responsibility
/ by Andrea Braides
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Cham
Name of Publisher, Distributor, etc.
: Springer International Publishing :Imprint: Springer,
Date of Publication, Distribution, etc.
, 2014.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XI, 174 p. 42 illus., online resource.
SERIES
Series Title
(Lecture Notes in Mathematics,0075-8434
Volume Designation
; 2094)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.
Text of Note
Introduction -- Global minimization -- Parameterized motion driven by global minimization -- Local minimization as a selection criterion -- Convergence of local minimizers -- Small-scale stability -- Minimizing movements -- Minimizing movements along a sequence of functionals -- Geometric minimizing movements -- Different time scales -- Stability theorems -- Index.?╗╣