**abstract:**
I would like to discuss some questions related to some semilinear equations driven by a nonlocal elliptic operator (for example, the Allen-Cahn equation, in which the classical Laplace operator is replaced by a fractional Laplacian).
In particular, I would like to study the qualitative properties of the solutions, such as symmetry, density estimates of the level set, asymptotic behaviors, etc., and their relation with surfaces that minimize the fractional perimeter.
The students may have some interest in these papers:

- a simple introduction to fractional objects

- the paper with Ovidiu Savin proving that there are no singular fractional minimal surfaces in the plane

- a review on fractional minimal surfaces (attached here, to appear as Springer proceedings for an Indam workshop in Cortona).

Wed 4 Jul, 10:00 - 11:00, Aula Dini

Valdinoci July 4th

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