Serrin's overdetermined theorem and weak Bernoulli laws without Alt--Caffarelli regularity

Yi Ru-Ya Zhang

We study distributional Bernoulli-type conditions in geometrically irregular domains $\Omega$. Here the zero extension of $u$ to ${\mathbb{R}}^n$ satisfies $$ Δu \;=\; c\,\mathcal{H}^{n-1…