Geodesic
On the maximum principle for strongly elliptic and parabolic second order systems with constant coefficients
Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 457-479 
V. G. Maz'ya; G. I. Kresin. On the maximum principle for strongly elliptic and parabolic second order systems with constant coefficients. Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 457-479. http://geodesic.mathdoc.fr/item/SM_1986_53_2_a10/
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     title = {On the maximum principle for strongly elliptic and parabolic second order systems with constant coefficients},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The question of validity of the classical maximum principle is considered for strongly elliptic and parabolic second order systems with constant coefficients. Bibliography: 14 titles.

[1] Miranda C., “Teorema del massimo modulo e teorema di esistenza e di unicitá per il problema di Dirichlet relativo alle equazioni ellitiche in due variabili”, Ann. Mat. Pure Appl., Ser. 4, 46 (1958), 265–311 | DOI | MR | Zbl

[2] Agmon S., “Maximum theorem for solutions of higher order elliptic equations”, Bull. Amer. Math. Soc., 66 (1960), 77–80 | DOI | MR | Zbl

[3] Shultse B. V., “Ob apriornykh otsenkakh v ravnomernykh normakh dlya silno ellipticheskikh sistem”, Sib. matem. zhurn., 16:2 (1975), 384–393

[4] Shapiro Z. Ya., “Pervaya kraevaya zadacha dlya ellipticheskoi sistemy differentsialnykh uravnenii”, Matem. sb., 28(70) (1951), 55–78. | Zbl

[5] Solonnikov V. A., “Ob obschikh kraevykh zadachakh dlya sistem, ellipticheskikh v smysle Duglisa–Nirenberga”, Izv. AN SSSR. Ser. matem., 28:3 (1964), 665–706 | MR

[6] Agmon S., Douglis A., Nirenberg L., “Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions. II”, Comm. Pure Appl. Math., 17:1 (1964), 35–92 | DOI | MR | Zbl

[7] Bitsadze A. V., “Ob ellipticheskikh sistemakh differentsialnykh uravnenii s chastnymi proizvodnymi vtorogo poryadka”, DAN SSSR, 112:6 (1957), 983–986 | MR | Zbl

[8] Polýa G., “Liegt die Stelle der grössten Beanspruchung an der Oberfläche?”, Zeitschr. Angew. Math. Mech., Bd. 10:4 (1930), 353–360 | DOI

[9] Eidelman S. D., Parabolicheskie sistemy, Nauka, M., 1964 | MR | Zbl

[10] Kupradze V. D., Gegelia T. G., Basheleishvili M. O., Burchuladze T. V., Trekhmernye zadachi matematicheskoi teorii uprugosti, Nauka, M., 1976 | MR

[11] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970 | MR

[12] Parton V. Z., Perlin P. I., Metody matematicheskoi teorii uprugosti, Nauka, M., 1981 | MR

[13] Miranda C., “Formule di maggiorazione e teorema di esistenza per le funzioni biarmoniche di due variabili”, Giorn. Mat. Battaglini, 78 (1948–1949), 97–118 | MR | Zbl

[14] Eidelman S. D., “O svyazi fundamentalnykh matrits reshenii parabolicheskikh i ellipticheskikh sistem”, Matem. sb., 35(77) (1954), 54–72 | MR