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010   $a3-319-01982-1
024 7 $a10.1007/978-3-319-01982-6
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035   $a(DE-He213)978-3-319-01982-6
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100   $a20131025d2014      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aLocal Minimization, Variational Evolution and ?-Convergence /$fby Andrea Braides
205   $a1st ed. 2014.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014.
215   $a1 online resource (XI, 174 p. 42 illus.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2094
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-01981-3 
327   $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.
330   $aThis book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2094
606   $aApplied mathematics
606   $aEngineering mathematics
606   $aPartial differential equations
606   $aCalculus of variations
606   $aApproximation theory
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aFunctional analysis
606   $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
606   $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
615  0$aApplied mathematics.
615  0$aEngineering mathematics.
615  0$aPartial differential equations.
615  0$aCalculus of variations.
615  0$aApproximation theory.
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615  0$aFunctional analysis.
615 14$aApplications of Mathematics.
615 24$aPartial Differential Equations.
615 24$aCalculus of Variations and Optimal Control; Optimization.
615 24$aApproximations and Expansions.
615 24$aAnalysis.
615 24$aFunctional Analysis.
676   $a515.64
700   $aBraides$b Andrea$4aut$4http://id.loc.gov/vocabulary/relators/aut$062002
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300151203321
996   $aLocal minimization, variational evolution and -convergence$91395527
997   $aUNINA