Mathematics - Colloquium
Friday, December 4, 2009
11:00 AM-12:00 PM
ABSTRACT: In this talk I will consider the following class of elliptic free boundary problems $Lu=-div(\chi(u)H(X))$, where $u$ and $\chi$ are nonnegative functions, $\chi=1$ a.e. in $[u>0]$, $L$ is a second order linear elliptic operator, $H=(H_1,H_2)$ is a vector function, and $X=(x,y)$.
When $H_1=0$ and $H_2$ is nondecreasing with respect to $y$, the free boundary $\partial[u>0]$ is the graph of a continuous curve $y=\Phi(x)$. I will discuss the situation when $H$ is a Lipschitz vector function with nonnegative divergence and show that the free boundary $\partial[u>0]$ can be represented locally by a family of continuous functions.
This is a joint work with S. Challal.
Suggested Audiences: Adult, College
Last Modified: November 10, 2009 at 4:09 PM