### 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.