Estimates of Holder constants for functions satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality with unbounded coefficients

One obtains inner and boundary estimates of the Hölder constants for functions $u(\cdot)$ satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality of nondivergence form with unbounded coefficients. It is shown that the Holder exponents in them depend only on the dimension $w$ and on the constants $\nu$ and $\mu$ occurring in the ellipticity conditions. In the boundary estimates they depend also on the constant $\theta_0$, occurring in the condition $(A)$ on the boundary and on the Holder exponent for the boundary values of $u(\cdot)$.