Seminario di analisi matematica
ore
11:30
presso Seminario I
I will present two (unconventional) overdetermined problems.
Let $n\geq 3$ and $\Omega$ be a bounded domain in $R^n$.
First: if the Newtonian potential $u$ of $\Omega$ has two homothetic convex level sets, then $\Omega$ is a ball.
Second: if the Newtonian potential $u$ of $\Omega$ is $\frac{1}{2-n}$-concave (i.e. $u^{(1/(2−n)}$ is convex), then Ω is a ball.
The result can be extend to the $p$-capacity potential for $p\in(1,n)$.