Published: Oct. 10, 2014

Liouville Theorems for α-harmonic functions in R^n and in a half space

Wenxiong Chen

Department of MathematicsYeshiva University

Date and time: 

Friday, October 10, 2014 - 3:00pm


ECCR 245


In recent years, the fractional Laplacian has seen more and more applications in mathematical physics and related fields, such as anomalous diffusion and quasi-geostrophic flows, turbulence models and water waves, molecular dynamics, and relativistic quantum mechanics of stars, as well as in probability and finance.

To study linear or nonlinear partial differential equations involving fractional Laplacians, the Liouville type theorems play an important role in obtaining a priori estimates, existence, and non-existence of solutions.

In this talk, I will present two Liouville type theorems–the uniqueness of α-harmonic functions– in the whole space R^n and in a half space. The ideas of proofs will be illustrated.

These are the joint works with Professor Congming Li, Yan Li, Lizhi Zhang, and Tingzhi Cheng.