Monge-Ampere Equation

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In recent years, the study of the Monge-Ampere equation has received consider- able attention and there have been many important advances. As a consequence there is nowadays much interest in this equation and its applications. This volume tries to r…

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    Om Monge-Ampere Equation

    In recent years, the study of the Monge-Ampere equation has received consider- able attention and there have been many important advances. As a consequence there is nowadays much interest in this equation and its applications. This volume tries to reflect these advances in an essentially self-contained systematic exposi- tion of the theory of weak: solutions, including recent regularity results by L. A. Caffarelli. The theory has a geometric flavor and uses some techniques from har- monic analysis such us covering lemmas and set decompositions. An overview of the contents of the book is as follows. We shall be concerned with the Monge- Ampere equation, which for a smooth function u, is given by (0.0.1) There is a notion of generalized or weak solution to (0.0.1): for u convex in a domain n, one can define a measure Mu in n such that if u is smooth, then Mu 2 has density det D u. Therefore u is a generalized solution of (0.0.1) if M u = f.

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    Detaljer

    Format
    E-Bok
    Kopisperre
    Teknisk DRM
    Filformat
    PDF
    Utgivelsesår
    2012
    Forlag
    Birkhauser Boston
    Språk
    Engelsk
    ISBN
    9781461201953

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