Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 90-107
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O. A. Ladyzhenskaya; N. N. Ural'tseva. On estimates of $\max|u_x|$ for solutions of quasilinear elliptic and parabolic equations of the general type and on some existence theorems. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 90-107. http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a6/
@article{ZNSL_1984_138_a6,
author = {O. A. Ladyzhenskaya and N. N. Ural'tseva},
title = {On estimates of $\max|u_x|$ for solutions of quasilinear elliptic and parabolic equations of the general type and on some existence theorems},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {90--107},
year = {1984},
volume = {138},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a6/}
}
TY - JOUR
AU - O. A. Ladyzhenskaya
AU - N. N. Ural'tseva
TI - On estimates of $\max|u_x|$ for solutions of quasilinear elliptic and parabolic equations of the general type and on some existence theorems
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1984
SP - 90
EP - 107
VL - 138
UR - http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a6/
LA - ru
ID - ZNSL_1984_138_a6
ER -
%0 Journal Article
%A O. A. Ladyzhenskaya
%A N. N. Ural'tseva
%T On estimates of $\max|u_x|$ for solutions of quasilinear elliptic and parabolic equations of the general type and on some existence theorems
%J Zapiski Nauchnykh Seminarov POMI
%D 1984
%P 90-107
%V 138
%U http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a6/
%G ru
%F ZNSL_1984_138_a6
A priori estimates of $\max|u_x|$ solutions of nondivergent quasilinear uniformly elliptic and parabolic equations are derived only under “natural” restrictions on the functions $a_{ij}$, on their first partial derivatives and on the function $a$. Some known existence theorems for the Dirichlet problem for elliptic equations are generalized.
