Geodesic
On the maximum principle for nonlinear parabolic and elliptic equations
Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 335-347.

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

A maximum principle in Sobolev spaces is proved for nonlinear elliptic and parabolic equations. The proof is based on estimates for the maximum of the solutions of a parabolic equation with measurable coefficients, in terms of the $\mathscr L_p$ norm of the right side. The results of the paper are analogous to results of A. D. Aleksandrov on elliptic equations. Bibliography: 10 titles. 
@article{IM2_1979_13_2_a6,
     author = {N. V. Krylov},
     title = {On the maximum principle for nonlinear parabolic and elliptic equations},
     journal = {Izvestiya. Mathematics },
     pages = {335--347},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1979},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a6/}
}
TY  - JOUR
AU  - N. V. Krylov
TI  - On the maximum principle for nonlinear parabolic and elliptic equations
JO  - Izvestiya. Mathematics 
PY  - 1979
SP  - 335
EP  - 347
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a6/
LA  - en
ID  - IM2_1979_13_2_a6
ER  - 
%0 Journal Article
%A N. V. Krylov
%T On the maximum principle for nonlinear parabolic and elliptic equations
%J Izvestiya. Mathematics 
%D 1979
%P 335-347
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a6/
%G en
%F IM2_1979_13_2_a6
N. V. Krylov. On the maximum principle for nonlinear parabolic and elliptic equations. Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 335-347. http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a6/

[1] Aleksandrov A. D., “Issledovaniya o printsipe maksimuma”, Izv. vyssh. uchebn. zaved., ser. matem., 1961, no. 1, 3–20

[2] Aleksandrov A. D., “Mazhorirovanie reshenii lineinykh uravnenii vtorogo poryadka”, Vestnik LGU, 1:1 (1966), 5–25 | MR | Zbl

[3] Krylov N. V., “K teorii nelineinykh vyrozhdayuschikhsya ellipticheskikh uravnenii”, Dokl. AN SSSR, 201:6 (1971), 1279–1281

[4] Krylov N. V., “Printsip maksimuma dlya parabolicheskikh uravnenii”, Uspekhi matem. nauk, 31:4 (1976), 267–268 | MR | Zbl

[5] Krylov N. V., Upravlyaemye protsessy diffuzionnogo tipa, Nauka, M., 1977 | MR

[6] Danford N., Shvarts Dzh. T., Lineinye operatory, obschaya teoriya, IL, M., 1962

[7] Krylov N. V., “Posledovatelnosti vypuklykh funktsii i otsenki maksimuma resheniya parabolicheskogo uravneniya”, Sib. matem. zhurnal, 17:2 (1976), 290–303 | MR | Zbl

[8] Krylov N. V., “Ob odnom klasse nelineinykh uravnenii v prostranstve izmerimykh funktsii”, Matem. sb., 80:2 (1969), 253–265 | MR | Zbl

[9] Oleinik O. A., “O lineinykh uravneniyakh vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Matem. sb., 69:1 (1966), 111–140 | MR | Zbl

[10] Oleinik O. A., Radkevich E. V., Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi, VINITI, M., 1971