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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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/
@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},
year = {1985},
volume = {147},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a5/}
}
TY - JOUR
AU - O. A. Ladyzhenskaya
AU - N. N. Ural'tseva
TI - Estimates of Holder constants for functions satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality with unbounded coefficients
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1985
SP - 72
EP - 94
VL - 147
UR - http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a5/
LA - ru
ID - ZNSL_1985_147_a5
ER -
%0 Journal Article
%A O. A. Ladyzhenskaya
%A N. N. Ural'tseva
%T Estimates of Holder constants for functions satisfying a uniformly elliptic or uniformly parabolic quasilinear inequality with unbounded coefficients
%J Zapiski Nauchnykh Seminarov POMI
%D 1985
%P 72-94
%V 147
%U http://geodesic.mathdoc.fr/item/ZNSL_1985_147_a5/
%G ru
%F ZNSL_1985_147_a5
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 $u(\cdot)$.
