Professor Joseph Iaia invites you to attend the Master's Project Defense of Siyu Gao.
When: Friday, October 22nd, at 8:45am in GAB 461
"Harmonic Function, the Mean Value Property and Perron's Method"
Abstract:
We discuss harmonic, subharmonic, and superharmonic functions and derive the mean value property for harmonic functions. We discuss the maximum principle for harmonic and subharmonic functions and we prove Liouville's theorem for harmonic functions.
We define the harmonic lifting of a subharmonic function and use this and Perron's method to find a harmonic function u in an open, bounded domain with Dirichlet boundary conditions.