Geodesic
Estimates of Holder constants for functions satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality with unbounded coefficients
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 17, Tome 147 (1985), pp. 72-94

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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 $u(\cdot)$. 
@article{ZNSL_1985_147_a5,
     author = {O. A. Ladyzhenskaya and N. N. Ural'tseva},
     title = {Estimates of {Holder} constants for functions satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality with unbounded coefficients},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {72--94},
     publisher = {mathdoc},
     volume = {147},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a5/}
}
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O. A. Ladyzhenskaya; N. N. Ural'tseva. Estimates of Holder constants for functions satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality with unbounded coefficients. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 17, Tome 147 (1985), pp. 72-94. http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a5/