Speaker: Feibai Ren
University of Notre Dame
Will give a Graduate Student Geometry Seminar entitled:
A Moving Planes Method for Nonlinear Equations
Abstract: In this talk, we discuss the method of moving planes in the analysis of nonlinear elliptic equations. Originally introduced by Alexandroff in 1962 to study the symmetry properties of surfaces, this technique was later extended by Gidas, Ni, and Nirenberg to classify positive solutions of the semilinear equation $-\Delta u=f(u)$ for some $C^1$ function $f$ on bounded domains. We will establish comparison results derived from the moving plane method, incorporating refined applications of maximum principles. We will also show that this technique can be applied to the resolution of conformally invariant equation $\Delta u+u^{\frac{n+2}{n-2}}=0$ on the whole space $\mathbb{R}^n$ where $n \geq 3$.
Date: 11-08-2024
Time: 4:00 pm
Location: 258 Hurley Bldg
Originally published at math.nd.edu.