LEADER 03931nam 22005535 450 001 9910135973803321 005 20200707023931.0 010 $a9783319433745 024 7 $a10.1007/978-3-319-43374-5 035 $a(CKB)3710000000911466 035 $a(DE-He213)978-3-319-43374-5 035 $a(MiAaPQ)EBC4723008 035 $a(PPN)196323584 035 $a(EXLCZ)993710000000911466 100 $a20161022d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Monge-Ampère Equation$b[electronic resource] /$fby Cristian E. Gutiérrez 205 $a2nd ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2016. 215 $a1 online resource (XIV, 216 p. 6 illus., 3 illus. in color.) 225 1 $aProgress in Nonlinear Differential Equations and Their Applications,$x1421-1750 ;$v89 311 $a3-319-43372-5 311 $a3-319-43374-1 320 $aIncludes bibliographical references and index. 327 $aGeneralized Solutions to Monge-Ampère Equations -- Uniformly Elliptic Equations in Nondivergence Form -- The Cross-sections of Monge-Ampère -- Convex Solutions of detDu=1 in Rn -- Regularity Theory for the Monge-Ampère Equation -- W^2,p Estimates for the Monge-Ampère Equation -- The Linearized Monge-Ampère Equation -- Interior Hölder Estimates for Second Derivatives -- References -- Index. 330 $aNow in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas and set decompositions. An effort is made to present complete proofs of all theorems, and examples and exercises are offered to further illustrate important concepts. Some of the topics considered include generalized solutions, non-divergence equations, cross sections, and convex solutions. New to this edition is a chapter on the linearized Monge-Ampère equation and a chapter on interior Hölder estimates for second derivatives. Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-Ampère-type equations and their diverse applications in the areas of differential geometry, the calculus of variations, optimization problems, optimal mass transport, and geometric optics. Both researchers and graduate students working on nonlinear differential equations and their applications will find this to be a useful and concise resource. 410 0$aProgress in Nonlinear Differential Equations and Their Applications,$x1421-1750 ;$v89 606 $aPartial differential equations 606 $aDifferential geometry 606 $aMathematical physics 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 615 0$aPartial differential equations. 615 0$aDifferential geometry. 615 0$aMathematical physics. 615 14$aPartial Differential Equations. 615 24$aDifferential Geometry. 615 24$aMathematical Applications in the Physical Sciences. 676 $a515.353 700 $aGutiérrez$b Cristian E$4aut$4http://id.loc.gov/vocabulary/relators/aut$066032 906 $aBOOK 912 $a9910135973803321 996 $aMonge-Ampere equation$9377993 997 $aUNINA