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.
Henrik Shahgholian
KTH Royal Institute of Technology
Panagiotis Souganidis
The University of Chicago


Henrik Shahgholian

Tel: 08-790 67 54


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