Yi-Yang Xiao

Universal H\"older estimates for stable solutions to semilinear equations of fractional order

We establish universal interior H\"older and fractional energy estimates for stable solutions of $(-\Delta)^su=f(u)$, $0<s<1$, with $f\in C^1_{\mathrm{loc}}(\mathbb{R})$ nonnegative and convex. The bounds depend only on a weighted $L^1$ norm of the solution and hold under optimal conditions on the dimension and the fra...