# FRB

## Seminar

### Interior regularity of solutions to elliptic fully nonlinear free boundary problems.

Minne, A (KTH - Royal Institute of Technology, Stockholm)
Tuesday 15 April 2014, 13:00-14:00

Discussion Room, Newton Institute

#### Abstract

We will consider $W^{2,n}(B_{1})$ solutions to the fully nonlinear elliptic problem \begin{equation*} \begin{cases} F(D^{2}u,x)=f(x) & \text{a.e. in }B_{1}\cap\Omega,\\ |D^{2}u|\le K & \text{a.e. in }B_{1}\backslash\Omega, \end{cases} \end{equation*} where $\Omega$ is an unknown open set and $K$ is a given constant. For $F$ convex and some regularity assumptions on $F$ and $f$, $C^{1,1}$ regularity of $u$ is proven in $B_{1/2}$.

#### Video

This talk has not been recorded because this was an informal session.