The Maximum Principle / by Patrizia Pucci, James Serrin.

Springer eBooks

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.

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.

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