Geodesic
On Inequalities of the Friedrichs type for Combined Domains
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 146-157.

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Integral inequalities of the Friedrichs type for combined domains with plane and cylindrical symmetries are proved. The optimal constants in the right-hand sides of the inequalities are found. These constants depend on physical and geometrical parameters of the domains. Some generalizations of these inequalities to domains of a different shape are considered.
Keywords: a priori estimate, Friedrichs inequality, variational problem. 
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Viktor K. Andreev. On Inequalities of the Friedrichs type for Combined Domains. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 146-157. http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a2/

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

[2] S. G. Mikhlin, Lineinye uravneniya v chastnykh proizvodnykh, Vysshaya shkola, M., 1977 | MR

[3] O. A. Ladyzhenskaya, Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[4] V. P. Mikhailov, Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976 | MR | Zbl

[5] D. Dzhozef, Ustoichivost dvizhenii zhidkosti, Mir, M., 1981

[6] V. S. Vladimirov, Uravneniya matematicheskoi fiziki, Nauka, M., 1976 | Zbl

[7] U. Miller, Simmetriya i razdelenie peremennykh, Mir, M., 1981 | MR | Zbl

[8] V. K. Andreev, “Ob odnoi sopryazhënnoi nachalno-kraevoi zadache”, Differentsialnye uravneniya, 44:5 (2008), 1–7

[9] V. K. Andreev, “Evolyutsiya sovmestnogo dvizheniya dvukh vyazkikh teploprovodnykh zhidkostei v ploskom sloe pod deistviem nestatsionarnogo perepada davleniya”, PMTF, 49:4 (2008), 94–107 | MR

[10] V. K. Andreev, “Nestatsionarnoe dvizhenie ploskikh sloëv vyazkikh zhidkostei s obschei granitsei razdela”, Vychislitelnye tekhnologii, 12:5 (2007), 23–30

[11] V. M. Alekseev, V. M. Tikhomirov, S. V. Fomin, Optimalnoe upravlenie, Nauka, M., 1979 | MR