LEADER 02805nmm a2200433 i 4500 001 991003324259707536 007 cr nn 008mamaa 008 170206s2014 sz | o j |||| 0|eng d 020 $a9783319019826 024 7 $a10.1007/978-3-319-01982-6$2doi 035 $ab14316043-39ule_inst 082 04$a519$223 084 $aAMS 49J45 084 $aAMS 74Q10 084 $aAMS 49J40 084 $aAMS 74Q05 100 1 $aBraides, Andrea$062002 245 10$aLocal Minimization, Variational Evolution and [Gamma]-Convergence$h[e-book] /$cby Andrea Braides 264 1$aCham :$bSpringer Intern. Publ.,$c2014 300 $a1 online resource (xi, 174 p. 42 : ill.) 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 347 $atext file$bPDF$2rda 490 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2094 505 0 $aIntroduction ; 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 520 3 $aThis book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed. 650 0$aGlobal analysis (Mathematics) 650 0$aFunctional analysis 650 0$aDifferential equations, Partial 650 0$aMathematical optimization 773 0 $aSpringer eBooks 776 08$aPrinted edition:$z9783319019819 856 40$uhttp://link.springer.com/book/10.1007/978-3-319-01982-6$zAn electronic book accessible through the World Wide Web 907 $a.b14316043$b03-03-22$c06-02-17 912 $a991003324259707536 996 $aLocal minimization, variational evolution and -convergence$91395527 997 $aUNISALENTO 998 $ale013$b06-02-17$cm$d@ $e-$feng$gsz $h0$i0