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

Inhalt
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.