I am curious about the Hölder exponent obtained by the De Giorgi-Nash-Moser theory, as a function of the ellipticity. More precisely: suppose $ u$ satisfies weakly $ $ D_i(a^{ij}D_ju)=f $ $ on the $ d$ -dimensional ball of radius $ R$ , with $ 0$ Dirichlet boundary conditions, with the matrix $ (a^{ij})_{i,j=1..d}$ bounded from below and above by $ \lambda I$ and $ \Lambda I$ , respectively, $ \lambda>0$ . For the right-hand side, let’s just take $ f\in L_\infty$ . Then we know that $ u\in C^{\alpha}(B_R)$ , with some $ \alpha=\alpha(d, \Lambda/\lambda)$ , my question is whether something about the dependence on $ \Lambda/\lambda$ is known. The analogous question for interior regularity (which might be easier) could also be of interest. Thanks!