A new symmetry criterion based on the distance function and applications to PDE's

Graziano Crasta, Ilaria Fragalà

We prove that, if $\Omega \subset {\mathbb{R}}^n$ is an open bounded starshaped domain of class $C^2$, the constancy over $\partial \Omega$ of the function $$φ(y) = \int_0^{λ(y)} \prod_{j=1}^{n…