Sign changing solutions of Poisson's equation

Michiel van den Berg, Dorin Bucur

Let $\Omega$ be an open, possibly unbounded, set in Euclidean space ${\mathbb{R}}^m$ with boundary $\partial \Omega ,$ let $A$ be a measurable subset of $\Omega$ with measure $|A|$, and let $\gamma \in (0,1)$. We…