Interior Hölder regularity for stable solutions to semilinear elliptic equations up to dimension 5

Fa Peng, Yi Ru-Ya Zhang, Yuan Zhou

Let $2\le n\le 5$. We establish an apriori interior Hölder regularity of $C^2$-stable solutions to the semilinear equation $-\Delta u=f(u)$ in any domain of $R^n$ for any nonlinearity $f…