LEADER 04063nam 22007455 450 001 9911015870603321 005 20251208192906.0 010 $a3-031-87202-9 024 7 $a10.1007/978-3-031-87202-0 035 $a(MiAaPQ)EBC32189447 035 $a(Au-PeEL)EBL32189447 035 $a(CKB)39567915000041 035 $a(OCoLC)1526859279 035 $a(DE-He213)978-3-031-87202-0 035 $a(PPN)287637565 035 $a(EXLCZ)9939567915000041 100 $a20250702d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aVariational and PDE Methods in Nonlinear Science $eCetraro, Italy 2023 /$fby Fabrice Bethuel, Duvan Henao, Angkana Rüland ; edited by Fabrice Bethuel, Giandomenico Orlandi, Bianca Stroffolini 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (0 pages) 225 1 $aC.I.M.E. Foundation Subseries,$x2946-1820 ;$v2366 311 08$a3-031-87201-0 327 $a- 1. Scalar and Vectorial Allen-Cahn Equations and their Asymptotics -- 2. Microstructures in the Modelling of Shape-Memory Alloys: Rigidity, Flexibility and Scaling -- 3. Singular Minimizers in Nonlinear Elasticity. 330 $aThis book presents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school ?Variational and PDE Methods in Nonlinear Science?, held in Cetraro (Italy), July 10?14, 2023. Fabrice Bethuel discusses aympototics for Allen?Cahn systems, providing an overview of classical methods and tools for the scalar case and further results for the two-dimensional vectorial case. An alternate monotonicity formula is described, and the still open parabolic vectorial case is considered. Angkana Rüland considers the modelling and analysis of microstructures in shape-memory alloys, including material on quasiconvexity, differential inclusions, rigidity of the two-well problem under BV-regularity assumptions, and recent results on the quantitative dichotomy between rigidity and flexibility. Duvan Henao focuses on existence theory in nonlinear elasticity, where a central role is played by the Jacobian determinant. The methods developed have implications for the analysis of magnetoelasticity and nematic elastomers. The volume is aimed at graduate students and researchers interested in the applications of PDEs and the calculus of variations to the theory of phase transitions, fluid dynamics, materials science, and elasticity theory. 410 0$aC.I.M.E. Foundation Subseries,$x2946-1820 ;$v2366 606 $aMathematical optimization 606 $aCalculus of variations 606 $aGeometry, Differential 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aFluid mechanics 606 $aCalculus of Variations and Optimization 606 $aDifferential Geometry 606 $aGlobal Analysis and Analysis on Manifolds 606 $aEngineering Fluid Dynamics 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aGeometry, Differential. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aFluid mechanics. 615 14$aCalculus of Variations and Optimization. 615 24$aDifferential Geometry. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aEngineering Fluid Dynamics. 676 $a519.6 676 $a515.64 700 $aBethuel$b Fabrice$042584 701 $aHenao$b Duvan$01833470 701 $aRu?land$b Angkana$00 701 $aOrlandi$b Giandomenico$01833472 701 $aStroffolini$b Bianca$01833473 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911015870603321 996 $aVariational and PDE Methods in Nonlinear Science$94408369 997 $aUNINA