LEADER 03720nam 22005055 450 001 9910770244803321 005 20240403175750.0 010 $a3-031-33928-2 024 7 $a10.1007/978-3-031-33928-8 035 $a(CKB)29310433000041 035 $a(MiAaPQ)EBC31001783 035 $a(Au-PeEL)EBL31001783 035 $a(DE-He213)978-3-031-33928-8 035 $a(EXLCZ)9929310433000041 100 $a20231206d2023 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPartial Differential Equations III $eNonlinear Equations /$fby Michael E. Taylor 205 $a3rd ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (774 pages) 225 1 $aApplied Mathematical Sciences,$x2196-968X ;$v117 311 08$a9783031339271 327 $aContents of Volumes I and II -- Preface -- 13 Function Space and Operator Theory for Nonlinear Analysis -- 14 Nonlinear Elliptic Equations -- 15 Nonlinear Parabolic Equations -- 16 Nonlinear Hyperbolic Equations -- 17 Euler and Navier?Stokes Equations for Incompressible Fluids -- 18 Einstein?s Equations -- Index. 330 $aThe third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: ?These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.? (Peter Lax, SIAM review, June 1998). 410 0$aApplied Mathematical Sciences,$x2196-968X ;$v117 606 $aDifferential equations 606 $aDifferential Equations 606 $aEquacions diferencials funcionals$2thub 608 $aLlibres electrònics$2thub 615 0$aDifferential equations. 615 14$aDifferential Equations. 615 7$aEquacions diferencials funcionals 676 $a515/.353 700 $aTaylor$b Michael E$041937 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910770244803321 996 $aPartial differential equations III$91492019 997 $aUNINA