On boundary value problems for elliptic systems of second-order equations in divergence form
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 2, pp. 93-103 Cet article a éte moissonné depuis la source Math-Net.Ru

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Solvability conditions of various boundary value problems for elliptic systems of second-order equations in divergence form are adduced. The effect of domain shape on the solvability of nonclassical problems of rigid contact and normal load is investigated in details. Particular attention is paid to the systems of equations of the type of stationary equations of linear elasticity, as well as to the systems of piezoelectrics theory.
Keywords: elliptic system of differential equations, coerciveness conditions, boundary value problem, solvability conditions.
Mots-clés : divergence form
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M. M. Karchevsky; R. R. Shagidullin. On boundary value problems for elliptic systems of second-order equations in divergence form. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 2, pp. 93-103. http://geodesic.mathdoc.fr/item/UZKU_2015_157_2_a7/

[1] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973, 407 pp. | MR

[2] Chipot M., Elliptic Equations: An Introductory Course, Birkhäuser, Basel, 2009, 290 pp. | MR | Zbl

[3] Nečas J., Direct Methods in the Theory of Elliptic Equations, Springer, Berlin–Heidelberg, 2012, 388 pp. | MR

[4] Besov O. V., “O koertsitivnosti v neizotropnom prostranstve S. L. Soboleva”, Matem. sb., 73(115):4 (1967), 585–599 | MR | Zbl

[5] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975, 482 pp. | MR

[6] Kardone Dzh., Korbo Espozito A., Nazarov S. A., “Osrednenie smeshannoi kraevoi zadachi dlya formalno samosopryazhennoi ellipticheskoi sistemy v periodicheskoi perforirovannoi oblasti”, Algebra i analiz, 21:4 (2009), 126–173 | MR | Zbl

[7] Amenzade Yu. A., Teoriya uprugosti, Vyssh. shk., M., 1976, 272 pp. | MR

[8] Dyuvo G., Lions Zh.-L., Neravenstva v mekhanike i fizike, Nauka, M., 1980, 384 pp. | MR

[9] Kondratev V. A., Oleinik O. A., “Kraevye zadachi dlya sistemy uravnenii teorii uprugosti v neogranichennykh oblastyakh. Neravenstva Korna”, Usp. matem. nauk, 43:5 (1988), 55–98 | MR | Zbl

[10] Parton V. Z., Kudryavtsev B. A., Elektrouprugost pezoelektricheskikh i elektroprovodnykh tel, Nauka, M., 1988, 472 pp.

[11] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977, 744 pp. | MR

[12] Gilbarg D., Trudinger H., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989, 464 pp. | MR

[13] Eidus D. M., “O smeshannoi zadache teorii uprugosti”, Dokl. AN SSSR, 76:2 (1951), 181–184 | MR

[14] Mikhlin S. G., Problema minimuma kvadratichnogo funktsionala, Gostekhizdat, M., 1952, 216 pp.

[15] Dubinskii Yu. A., “Some Coercive Problems for the System of Poisson Equations”, Russ. J. Math. Phys., 20:4 (2013), 402–412 | DOI | MR | Zbl

[16] Dubinskii Yu. A., “O nekotorykh granichnykh zadachakh dlya sistem uravnenii Puassona v trekhmernoi oblasti”, Differents. uravneniya, 49:5 (2013), 610–613 | MR | Zbl