The Maximum Principle

Patrizia Pucci, James Serrin (auth.)3764381442, 978-3-7643-8144-8, 9783764381455

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.

Table of contents :
Front Matter….Pages i-x
Introduction and Preliminaries….Pages 1-11
Tangency and Comparison Theorems for Elliptic Inequalities….Pages 13-49
Maximum Principles for Divergence Structure Elliptic Differential Inequalities….Pages 51-82
Boundary Value Problems for Nonlinear Ordinary Differential Equations….Pages 83-101
The Strong Maximum Principle and the Compact Support Principle….Pages 103-126
Non-homogeneous Divergence Structure Inequalities….Pages 127-151
The Harnack Inequality….Pages 153-180
Applications….Pages 181-221
Back Matter….Pages 223-235