Elliptic Differential Equations and Obstacle Problems

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Springer Science & Business Media, 31.07.1987 - 353 Seiten
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In the few years since their appearance in the mid-sixties, variational inequalities have developed to such an extent and so thoroughly that they may now be considered an "institutional" development of the theory of differential equations (with appreciable feedback as will be shown). This book was written in the light of these considerations both in regard to the choice of topics and to their treatment. In short, roughly speaking my intention was to write a book on second-order elliptic operators, with the first half of the book, as might be expected, dedicated to function spaces and to linear theory whereas the second, nonlinear half would deal with variational inequalities and non variational obstacle problems, rather than, for example, with quasilinear or fully nonlinear equations (with a few exceptions to which I shall return later). This approach has led me to omit any mention of "physical" motivations in the wide sense of the term, in spite of their historical and continuing importance in the development of variational inequalities. I here addressed myself to a potential reader more or less aware of the significant role of variational inequalities in numerous fields of applied mathematics who could use an analytic presentation of the fundamental theory, which would be as general and self-contained as possible.
  

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Inhalt

II
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VII
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VIII
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IX
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LVIII
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LIX
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LXVI
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XCIX
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Häufige Begriffe und Wortgruppen

Beliebte Passagen

Seite 345 - Existence and multiplicity theorems for semilinear elliptic equations with nonlinear boundary conditions.
Seite 343 - Duvaut G. and Lions J.-L. Inequalities in mechanics and physics. SpringerVerlag. Berlin and New York.
Seite 345 - Kazdan, JL, and Kramer, RJ Invariant criteria for existence of solutions to second-order quasilinear elliptic equations. Commun. Pure Appl. Math. 31, 619645 (1978).
Seite 343 - Irregular obstacles and quasi-variational inequalities of stochastic impulse control, Ann. Scuola Norm. Sup. Pisa Cl.
Seite 345 - John, F., and Nirenberg, L. On functions of bounded mean oscillation, Commun.
Seite 344 - Bilateral evolution problems of non-variational type: existence, uniqueness, Holder-regularity and approximation of solutions, Manuscripta Math.
Seite 347 - Moser, J. On Harnack's theorem for elliptic differential equations, Commun. Pure Appl. Math. 14, 577-591 (1961).
Seite 344 - Giaquinta, M. Remarks on the regularity of weak solutions to some variational inequalities, Math. Z. 177, 15-31 (1981).

Verweise auf dieses Buch

Elements of Nonlinear Analysis
Michel Chipot
Eingeschränkte Leseprobe - 2000
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