rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: Monge-Ampère Equation
  name:
    name part: Gutiérrez, Cristian E.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    edition: 2nd ed. 2016.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 216 p. 6 illus., 3 illus. in color. online resource.
  abstract: Now 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.
  table of contents: Generalized 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.
  note: by Cristian E. Gutiérrez.
  subject:
    topic: Mathematics
  subject:
    topic: Partial differential equations
  subject:
    topic: Mathematical physics
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Differential Geometry
  subject:
    topic: Mathematical Applications in the Physical Sciences
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Progress in Nonlinear Differential Equations and Their Applications, 89
  identifier: 9783319433745
  identifier: http://dx.doi.org/10.1007/978-3-319-43374-5
  record info:
    record creation date: 161022
    record change date: 20170413061531.0
    record identifier: 978-3-319-43374-5