Yuxuan Zhou

Interior Regularity for Stable Solutions of Semilinear Elliptic Equations with Sign-Changing Nonlinearities

We investigate interior regularity for stable solutions of the semilinear elliptic equation $-\Delta u=f(u)$ in an open set $\Omega\subseteq \mathbb R^n$, where $f$ is locally Lipschitz and may change sign. We establish sharp interior H\"older estimates for stable classical solutions in every dimension $n\le 9$, thereb...