Holder regularity for solutions to the Poisson equation

Question

I am dealing with a nonlinear PDE of the form $$-\Delta u=f(u),\quad in\,\,\,\mathbb{R}^n$$ (where $f(u)$ is a nonliear function) I would like to ask you which regularity results do exist in the case when $f\in C^{0,\theta}$. Thank you!