Second and Fourth Order Nonlinear Eigenvalue Problems

Dr. Craig Cowan

Department of Mathematics
Stanford University

15 March 2012
205 Shelby Center
2:30 (Refreshements at 2:00)

Abstract

In this talk we will examine various second and fourth order nonlinear elliptic partial differential equations which contain a parameter which is varied. Our interest is in how the value of the parameter affects the various properties of the solution(s) of the equation. We will mostly concentrate on the question of the regularity of the so called extremal solution. Many physical models have stationary states which fit into the framework of nonlinear eigenvalue problems.