| Abstract: |
| The aim of this talk is twofold. First, when dimension $n\le9$ and the nonlinearities $f$ changes sign, we will study the boundness of stable solutions to semilinear elliptic equations $-\Delta u=f(u)$. When dimension $n\ge 10$ and $f\ge 0$, we shall prove the sharp BMO and Morrey regularity for stable solutions. Second, as an application, we show a sharp Liouville property for stable solutions when dimension $n\ge 10$. This work is a collaboration with Prof. Yi Ru-Ya Zhang and Yuan Zhou. |
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