This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame (IN). Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear, however, the presented methods also apply to nonlinear problems.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Readership

Graduate students and research mathematicians interested in partial differential equations.

Table of Contents

• Harmonic functions
• Maximum principles
• Weak solutions, part I
• Weak solutions, part II
• Viscosity solutions
• Bibliography