The Maximum Principle
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Beschreibung
Intended for a wide audience, this 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. It is the first book containing a detailed description of modern work on the maximum principle for nonlinear elliptic differential 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.
The only book containing a detailed description of modern work on the maximum principle for nonlinear elliptic differential equations Contains applications to the celebrated symmetry question, to elliptic dead core phenomena, uniqueness theorems, the Harnack inequality and the compact support principle Includes supplementary material: sn.pub/extras
Autor*in
Patrizia Pucci
Themen in »The Maximum Principle«
Boundary value problem differential equation inequalities maximum maximum principle ordinary differential equation potential theory partial differential equations
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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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