MENU

You are here

Allen-Cahn equation and minimal surfaces

Speaker: 
Matteo Rizzi
Institution: 
SISSA
Schedule: 
Wednesday, May 25, 2016 - 16:30
Location: 
A-133
Abstract: 

In the talk I would like to discuss the links between the Allen-Cahn equation in R^N and minimal graphs. A celebrated conjecture due to De Giorgi asserts that any solition u satisfying |u|<1 and monotone in one direction must be one dimensional, in the sense that the level sets are hyperplanes, at least in dimension N ≤ 8. In dimension N=9, a counter example was constructed by Del Pino, Kowalczyk and Wei. I would like to give the outlines of the situation about the problem and to discuss what may happen in higher dimension.

Sign in