Quantitative bounds for Hölder exponents in the Krylov--Safonov and Evans--Krylov theories

We establish quantitative bounds for Hölder exponents in the Krylov–Safonov and Evans–Krylov theories when the ellipticity ratio is close to one. Our analysis relies on the Ishii–Lions method for the Krylov–Safonov theory and a Schauder-type perturbation argument for the Evans–Krylov theory.