Abstract
One obtains inner and boundary estimates of the Hölder constants for functions u(·) satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality of nondivergence form with unbounded coefficients. It is shown that the Hölder exponents in them depend only on the dimension W and on the constantsγ and μ occurring in the ellipticity conditions. In the boundary estimates they depend also on the constant θ0, occurring in the condition (A) on the boundary and on the Hölder exponent for the boundary values of u(·).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 72–94, 1985.
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Ladyzhenskaya, O.A., Ural'tseva, N.N. Estimates of the Hölder constant for functions satisfying a uniformly elliptic or a uniformly parabolic quasilinear inequality with unbounded coefficients. J Math Sci 37, 837–851 (1987). https://doi.org/10.1007/BF01387722
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DOI: https://doi.org/10.1007/BF01387722