Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.
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Maximum principles are bedrock results in the theory of second order elliptic equations. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.
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and Preliminaries.- Tangency and Comparison Theorems for Elliptic Inequalities.- Maximum Principles for Divergence Structure Elliptic Differential Inequalities.- Boundary Value Problems for Nonlinear Ordinary Differential Equations.- The Strong Maximum Principle and the Compact Support Principle.- Non-homogeneous Divergence Structure Inequalities.- The Harnack Inequality.- Applications.
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Aus den Rezensionen: “Das Maximumprinzip ist das stärkste Hilfsmittel, um Eindeutigkeit und stetige Abhängigkeit der Lösungen skalarer elliptischer und parabolischer Differentialgleichungen 2. Ordnung zu beweisen. ... In der Tat geht das Buch von Pucci-Serrin das Thema von Neuem an: Schwache Lösungen und Sobolewräume werden verwendet … Ohne Übertreibung kann das Buch als Juwel in der Reihe ‘Progress in Nonlinear Differential Equations and Their Applications‘ bezeichnet werden ...“ (N.Ortner, in: IMN Internationale Mathematische Nachrichten, April/2010, Issue 213, S. 55)
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The only book containing a detailed description of modern work on the maximum principle for nonlinear elliptic differential equationsContains applications to the celebrated symmetry question, to elliptic dead core phenomena, uniqueness theorems, the Harnack inequality and the compact support principleIncludes supplementary material: sn.pub/extras
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Produktdetaljer

ISBN
9783764381448
Publisert
2007-09-17
Utgiver
Vendor
Birkhauser Verlag AG
Vekt
1170 gr
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, UP, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet