Andrea Braides

Local Minimization, Variational Evolution and ¿-Convergence

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Lecture Notes in Mathematics 2094
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-01981-9
• 2014
• Seitenzahl: 188
• Erscheinungstermin: 12. November 2013
• Englisch
• Abmessung: 235mm x 155mm x 11mm
• Gewicht: 302g
• ISBN-13: 9783319019819
• ISBN-10: 3319019813
• Artikelnr.: 39158475

Inhaltsangabe

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.

Rezensionen

"The volume is carefully written and the material is organized in such a way that a Ph.D. student can gradually become familiar with -convergence analysis and related tools. When possible, one-dimensional examples are chosen to illustrate the topics and several figures help the reader follow the presentation. The volume is very suitable for a Ph.D. course devoted to an audience with a good background in functional analysis, function spaces, and variational problems." (Giuseppe Buttazzo, Mathematical Reviews, August, 2014)