LEADER 04156nam 22007095 450 001 9910770275003321 005 20240619170202.0 010 $a9783031450365$b(electronic bk.) 010 $z9783031450358 024 7 $a10.1007/978-3-031-45036-5 035 $a(MiAaPQ)EBC31024478 035 $a(Au-PeEL)EBL31024478 035 $a(DE-He213)978-3-031-45036-5 035 $a(CKB)29434930900041 035 $a(EXLCZ)9929434930900041 100 $a20231217d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Course in the Calculus of Variations $eOptimization, Regularity, and Modeling /$fby Filippo Santambrogio 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (354 pages) 225 1 $aUniversitext,$x2191-6675 311 08$aPrint version: Santambrogio, Filippo A Course in the Calculus of Variations Cham : Springer International Publishing AG,c2024 9783031450358 327 $a1 One-dimensional variational problems -- 2 Multi-dimensional variational problems -- 3 Lower semicontinuity -- 4 Convexity and its applications -- 5 Hölder regularity -- 6 Variational problems for sets -- 7 ?-convergence: theory and examples. 330 $aThis book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present. Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of ?-convergence. While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes. 410 0$aUniversitext,$x2191-6675 606 $aMathematical optimization 606 $aCalculus of variations 606 $aFunctional analysis 606 $aDifferential equations 606 $aCalculus of Variations and Optimization 606 $aFunctional Analysis 606 $aDifferential Equations 606 $aAnàlisi funcional$2thub 606 $aOptimització matemàtica$2thub 606 $aEquacions diferencials funcionals$2thub 606 $aCàlcul de variacions$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aFunctional analysis. 615 0$aDifferential equations. 615 14$aCalculus of Variations and Optimization. 615 24$aFunctional Analysis. 615 24$aDifferential Equations. 615 7$aAnàlisi funcional 615 7$aOptimització matemàtica 615 7$aEquacions diferencials funcionals 615 7$aCàlcul de variacions 676 $a519.6 676 $a515.64 700 $aSantambrogio$b Filippo$0742112 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910770275003321 996 $aA Course in the Calculus of Variations$93660739 997 $aUNINA