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Soave: Monotonicity and symmetry of solutions with uniform limits for some elliptic systems

Soave:
I will present some results regarding sharp a priori bounds, Liouville-type theorems, monotonicity and $1$-dimensional symmetry for solutions of the two systems

$
-\Delta u =u-u^3-\Lambda uv^2$ in $\mathbb{R}^N;$
$
-\Delta v =v-v^3-\Lambda u^2v$ in $\mathbb{R}^N$,
$u,v \ge 0$ in $\mathbb{R}^N$, with $\Lambda > 0$,

and

$
-\Delta u \, =-uv^2$ in $\mathbb{R}^N;$
$
-\Delta v \, =-u^2v$ in $\mathbb{R}^N$,
$u,v \ge 0$ in $\mathbb{R}^N$,


under suitable assumptions on the behavior of $u$ and $v$ when $x_N \to \pm \infty$. The talk is based on joint works with Alberto Farina, Berardino Sciunzi and Susanna Terracini.
http://cvgmt.sns.it/seminar/598/

When
Mon Oct 30, 2017 2pm – 3pm Coordinated Universal Time
Where
Scuola Normale Superiore, Aula Tonelli (map)