The Maximum Principle [Hardcover]

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.

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.

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.Aus den Rezensionen:Das Maximumprinzip ist das st?rkste Hilfsmittel, um Eindeutigkeit und stetige Abh?ngigkeit der L?sungen skalarer elliptischer und parabolischer Differentialgleichungen 2. Ordnung zu beweisen. ... In der Tat geht das Buch von Pucci-Serrin das Thema von Neuem an: Schwache L?sungen und Sobolewr?ume werden verwendet & Ohne ?bertreibung 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)

The only book containing a detaló+