04517nam 22008295 450 991030015120332120200630073424.03-319-01982-110.1007/978-3-319-01982-6(CKB)3710000000078587(DE-He213)978-3-319-01982-6(SSID)ssj0001049518(PQKBManifestationID)11550230(PQKBTitleCode)TC0001049518(PQKBWorkID)11036784(PQKB)10694606(MiAaPQ)EBC3107038(PPN)176105174(EXLCZ)99371000000007858720131025d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierLocal Minimization, Variational Evolution and Γ-Convergence /by Andrea Braides1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (XI, 174 p. 42 illus.)Lecture Notes in Mathematics,0075-8434 ;2094Bibliographic Level Mode of Issuance: Monograph3-319-01981-3 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.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.Lecture Notes in Mathematics,0075-8434 ;2094Applied mathematicsEngineering mathematicsPartial differential equationsCalculus of variationsApproximation theoryMathematical analysisAnalysis (Mathematics)Functional analysisApplications of Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M13003Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Calculus of Variations and Optimal Control; Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26016Approximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Applied mathematics.Engineering mathematics.Partial differential equations.Calculus of variations.Approximation theory.Mathematical analysis.Analysis (Mathematics).Functional analysis.Applications of Mathematics.Partial Differential Equations.Calculus of Variations and Optimal Control; Optimization.Approximations and Expansions.Analysis.Functional Analysis.515.64Braides Andreaauthttp://id.loc.gov/vocabulary/relators/aut62002MiAaPQMiAaPQMiAaPQBOOK9910300151203321Local minimization, variational evolution and -convergence1395527UNINA