LEADER 03863nam 22005655 450 001 9910999791903321 005 20250430130233.0 010 $a3-031-87164-2 024 7 $a10.1007/978-3-031-87164-1 035 $a(CKB)38672163000041 035 $a(DE-He213)978-3-031-87164-1 035 $a(MiAaPQ)EBC32086061 035 $a(Au-PeEL)EBL32086061 035 $a(OCoLC)1523372264 035 $a(EXLCZ)9938672163000041 100 $a20250430d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHandbook of Calculus of Variations for Absolute Beginners /$fby Lorenzo Brasco 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (XXVII, 610 p. 33 illus., 13 illus. in color.) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v163 311 08$a3-031-87163-4 327 $a- 1. Tools -- 2. Some One-Dimensional Variational Problems -- 3. Sobolev Spaces -- 4. The Direct Method in Sobolev Spaces -- 5. Lipschitz Functions -- 6. The Direct Method in Lipschitz Spaces -- 7. Excerpts from Regularity Theory -- 8. Solutions to Problems. 330 $aThe book aims at endowing any student with a survival toolkit to start safely diving into the realm of Calculus of Variations. In summary, the latter is a part of mathematical analysis devoted to minimization/maximization problems. A great effort has been made to present the themes and methods considered in the book in the simplest possible way: the reader will not find here general statements or proofs based on general abstract theories. In contrast, the main focus of the book is on introducing some key concepts "from scratch", by means of simple and meaningful explicit examples (including for instance, the classical isoperimetric and brachistocrone problems, as well as the boundary value problem for harmonic functions). In particular, the book is mainly (but not exclusively) designed to smoothly introduce the reader to the so-called Direct Method of the Calculus of Variations, which is a central concept in the field. Accordingly, a good part of the book is devoted to discussing spaces of weakly differentiable functions (i.e., Sobolev and Lipschitz functions), which are essential tools of the Direct Method. A long list of problems will guide the student through the study of the subject. Almost all the problems come with their fully detailed solutions. The book is complemented by four appendices, which contribute to making it self-contained, as well as to deepening the study of certain parts. Despite being designed for students, even the researchers in the field could find a reading of the book profitable, at least for certain parts concerning the properties of Sobolev spaces, functional inequalities of the Sobolev-Poincaré type, tricks to handle nonlinear elliptic PDEs, and a gentle introduction to some techniques of modern regularity theory for elliptic PDEs. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v163 606 $aMathematical optimization 606 $aCalculus of variations 606 $aMathematical analysis 606 $aCalculus of Variations and Optimization 606 $aAnalysis 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aMathematical analysis. 615 14$aCalculus of Variations and Optimization. 615 24$aAnalysis. 676 $a519.6 676 $a515.64 700 $aBrasco$b Lorenzo$4aut$4http://id.loc.gov/vocabulary/relators/aut$01817610 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910999791903321 996 $aHandbook of Calculus of Variations for Absolute Beginners$94375539 997 $aUNINA