LEADER 03600nam 22006375 450 001 9910743693503321 005 20240619151504.0 010 $a3-031-35976-3 024 7 $a10.1007/978-3-031-35976-7 035 $a(CKB)28103158600041 035 $a(MiAaPQ)EBC30723212 035 $a(Au-PeEL)EBL30723212 035 $a(DE-He213)978-3-031-35976-7 035 $a(PPN)272261297 035 $a(EXLCZ)9928103158600041 100 $a20230829d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Compact Course on Linear PDEs /$fby Alberto Valli 205 $a2nd ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (267 pages) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v154 311 $a9783031359750 327 $a1. Introduction -- 2. Second order linear elliptic equations -- 3. A bit of functional analysis -- 4. Weak derivatives and Sobolev spaces -- 5. Weak formulation of elliptic PDEs -- 6. Technical results -- 7. Additional results -- 8. Saddle points problems -- 9. Parabolic PDEs -- 10. Hyperbolic PDEs -- Appendix A: Partition of unity -- Appendix B: Lipschitz continuous and smooth domains -- Appendix C: Integration by parts for smooth functions and vector ?elds -- Appendix D: Reynolds transport theorem -- Appendix E: Gronwall lemma -- Appendix F: Necessary and su?cient conditions for the well-posedness of the variational problem. 330 $aThis textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations. . 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v154 606 $aDifferential equations 606 $aMathematics$xData processing 606 $aFunctional analysis 606 $aDifferential Equations 606 $aComputational Mathematics and Numerical Analysis 606 $aFunctional Analysis 606 $aEquacions en derivades parcials$2thub 606 $aAnàlisi funcional$2thub 608 $aLlibres electrònics$2thub 615 0$aDifferential equations. 615 0$aMathematics$xData processing. 615 0$aFunctional analysis. 615 14$aDifferential Equations. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aFunctional Analysis. 615 7$aEquacions en derivades parcials 615 7$aAnàlisi funcional 676 $a515.353 700 $aValli$b Alberto$08376 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910743693503321 996 $aCompact Course on Linear PDEs$92983604 997 $aUNINA