On the De Giorgi conjecture in half spaces

  • John Anderson (Royal Institute of Technology, Stockholm)
Felix-Klein-Hörsaal (Raum 4-24) Universität Leipzig (Leipzig)


In 1978 E. De Giorgi conjectured that the only bounded solutions of $\Delta u = u^3 - u$ in the entire space $\mathbb R^n$ , with strictly positive derivative in one direction, are one dimentional. At least if $n \le 8$. This conjecture has been given a considerable attention in the recent years. And a weak version of it was recently proven by O. Savin. In this talk we will introduce the conjecture, discuss some of its history and show that it isn't true if $\mathbb R^n$ is changed to the upper half space $\mathbb R{^n _+}$.

5/4/00 11/9/06


Universität Leipzig Felix-Klein-Hörsaal

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail