Colloquium Lectures
Special Lecture, Friday November 6, 10AM, 128DH
Speaker: Scott Armstrong
Title: Fundamental solutions of fully nonlinear elliptic PDE
Time: 10AM Friday November 6, DH 128
Abstract:
I will present results on the existence and uniqueness of
fundamental solutions of positively homogeneous, fully nonlinear
elliptic equations like the Bellman-Isaacs equation. The methods we
use are inspired by the recently developed principal eigenvalue theory
for fully nonlinear equations. Using blow-up arguments, we demonstrate
that the fundamental solutions characterize the isolated singularities
of solutions which are bounded on one side. As another application, we
show that the "intrinsic scaling exponent" derived from the
fundamental solution characterizes whether an associated stochastic
process, controlled by two competing players, is recurrent or
transient. This work is joint with B. Sirakov and C. K. Smart.
