On a conjecture of De Giorgi related to homogenisation
Homogenization and Random Phenomenon
27 November 15:00 - 15:55
Aram Karakhanyan - University of Edinburgh
In this talk a will discuss some problems related to homogenisation of first order systems of ODEs with oscillating structures. A typical example would be $y'=F(y/\epsilon)$ where $F$ is a smooth, periodic vector field and $\epsilon>0$ a small parameter. In 1994 E. De Giorgi conjectured that $y_0$, the limit of $y$ as $\epsilon \to 0$, must be a linear function. This is proved in 1 and 2 dimensions for general flow generated by $F$ and in higher dimensions for the shear flow. The results to be presented are from a joint work with H. Shahgholian.
KTH Royal Institute of Technology
The University of Chicago