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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 $-Δu=f(u)$ in an open set $Ω\subseteq \mathbb R^n$, where $f$ is locally Lipschitz and may change sign. We establish sharp interior Hölder estimates for stable classical solutions in every dimension $n\le 9$,
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