**AMS-MAA Joint Lecture Series** 1992; 60 minutes; VHS ISBN-10: 0-8218-8077-2 ISBN-13: 978-0-8218-8077-7 List Price: US$49.95 Individual Members: US$39.96 Institutional Members: US$37.46 Order Code: VIDEO/82
| Roughly speaking, the maximum principle asserts that under certain conditions, a solution of a linear elliptic equation (or inequality) assumes its maximum on the boundary of its domain. For years this principle has proven to be an extremely useful and flexible tool in the study of nonlinear and linear equations. New and sufficient conditions for the maximum principle, and new variations on it, are constantly being discovered. This videotape captures a lecture on the maximum principle by the celebrated analyst Louis Nirenberg. Nirenberg explains the method of moving planes and how the maximum principle provides a simplified approach to this method. He then uses this method to prove symmetry and monotonicity of solutions of certain boundary value problems. Exceptional in clarity of presentation, this lecture starts with the fundamentals and concludes with an intriguing and nontrivial problem that demonstrates the power of the maximum principle. This videotape is an excellent supplement for a course in analysis or differential equations and is accessible to undergraduate mathematics majors. |