Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@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},
     publisher = {mathdoc},
     volume = {138},
     year = {1984},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a6/
%G ru
%F ZNSL_1984_138_a6
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/