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.

Contenu
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.