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Birkhäuser

The Maximum Principle

  • Book
  • © 2007

Overview

Authors:
  1. Patrizia Pucci

    1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy

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    You can also search for this author in PubMed   Google Scholar

  2. James Serrin

    1. Department of Mathematics, University of Minnesota, Minneapolis, USA

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    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 73)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction and Preliminaries

    Pages 1-11

  3. Tangency and Comparison Theorems for Elliptic Inequalities

    Pages 13-49

  4. Maximum Principles for Divergence Structure Elliptic Differential Inequalities

    Pages 51-82

  5. Boundary Value Problems for Nonlinear Ordinary Differential Equations

    Pages 83-101

  6. The Strong Maximum Principle and the Compact Support Principle

    Pages 103-126

  7. Non-homogeneous Divergence Structure Inequalities

    Pages 127-151

  8. The Harnack Inequality

    Pages 153-180

  9. Applications

    Pages 181-221

  10. Back Matter

    Pages 223-235
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Keywords

About this book

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.

Reviews

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)

Authors and Affiliations

  • Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy

    Patrizia Pucci

  • Department of Mathematics, University of Minnesota, Minneapolis, USA

    James Serrin

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