03531nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184072001600207082001600223100007200239245022400311250001800535264007500553300006400628336002600692337002600718338003600744347002400780490005300804520119500857650003602052650002802088650002702116650011202143650013802255650010302393700008002496700007502576700008002651700007502731710003402806773002602840776003602866776003602902830005302938856004602991978-3-319-54208-9DE-He21320210120150115.0cr nn 008mamaa170615s2017 gw | s |||| 0|eng d a97833195420897 a10.1007/978-3-319-54208-92doi 4aQA370-380 7aPBKJ2bicssc 7aMAT0070002bisacsh 7aPBKJ2thema04a515.3532231 aLe, Nam Q.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aDynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equationsh[electronic resource] :bVIASM 2016 /cby Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran. a1st ed. 2017. 1aCham :bSpringer International Publishing :bImprint: Springer,c2017. aVII, 228 p. 16 illus., 1 illus. in color.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aLecture Notes in Mathematics,x0075-8434 ;v2183 aConsisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the nonlinear adjoint method, is introduced. The appendix offers a short introduction to the theory of viscosity solutions of first-order Hamilton–Jacobi equations. . 0aPartial differential equations. 0aCalculus of variations. 0aDifferential geometry.14aPartial Differential Equations.0https://scigraph.springernature.com/ontologies/product-market-codes/M1215524aCalculus of Variations and Optimal Control; Optimization.0https://scigraph.springernature.com/ontologies/product-market-codes/M2601624aDifferential Geometry.0https://scigraph.springernature.com/ontologies/product-market-codes/M210221 aMitake, Hiroyoshi.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aTran, Hung V.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aMitake, Hiroyoshi.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aTran, Hung V.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978331954207208iPrinted edition:z9783319542096 0aLecture Notes in Mathematics,x0075-8434 ;v218340uhttps://doi.org/10.1007/978-3-319-54208-9