02805nmm a2200433 i 4500991003324259707536cr nn 008mamaa170206s2014 sz | o j |||| 0|eng d978331901982610.1007/978-3-319-01982-6doib14316043-39ule_inst51923AMS 49J45AMS 74Q10AMS 49J40AMS 74Q05Braides, Andrea62002Local Minimization, Variational Evolution and [Gamma]-Convergence[e-book] /by Andrea BraidesCham :Springer Intern. Publ.,20141 online resource (xi, 174 p. 42 : ill.)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture Notes in Mathematics,1617-9692 ;2094Introduction ; 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 ; IndexThis 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.Global analysis (Mathematics)Functional analysisDifferential equations, PartialMathematical optimizationSpringer eBooksPrinted edition:9783319019819http://link.springer.com/book/10.1007/978-3-319-01982-6An electronic book accessible through the World Wide Web.b1431604303-03-2206-02-17991003324259707536Local minimization, variational evolution and -convergence1395527UNISALENTOle01306-02-17m@ -engsz 00