Geodesic
On boundary-value problems for second-order elliptic and parabolic systems
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 1, Tome 58 (2015), pp. 43-58 
E. V. Golubeva; Yu. A. Dubinskii. On boundary-value problems for second-order elliptic and parabolic systems. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 1, Tome 58 (2015), pp. 43-58. http://geodesic.mathdoc.fr/item/CMFD_2015_58_a2/
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     author = {E. V. Golubeva and Yu. A. Dubinskii},
     title = {On boundary-value problems for second-order elliptic and parabolic systems},
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     year = {2015},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2015_58_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For nonstandard boundary-value problems for systems of equations of elliptic and parabolic types with vector boundary conditions, the well-posedness is proved. Typical examples are provided.

[1] Dubinskii Yu. A., “Razlozhenie sobolevskoi shkaly i gradientno-divergentnoi shkaly v summu solenoidalnykh i potentsialnykh podprostranstv”, Tr. MIAN, 255, 2005, 136–145 | MR

[2] Dubinskii Yu. A., “O nekotorykh kraevykh zadachakh dlya sistemy uravnenii Puassona v trekhmernoi oblasti”, Diff. uravn., 49:5 (2013), 610–613 | MR | Zbl

[3] Dubinskii Yu. A., “Ob odnoi kraevoi zadache dlya statsionarnoi sistemy uravnenii Stoksa”, Vestn. MEI, 2014, no. 1, 94–98

[4] Dubinskii Yu. A., “O nekotorykh zadachakh dlya sistem uravnenii Puassona i Stoksa”, Abstracts of the Seventh Int. Conf. on Differ. and Funct. Differ. Equ. (Moscow, Russia, August 21–28, 2014), 140

[5] Golubeva E. V., “Kraevaya zadacha dlya sistemy uravnenii Puassona v dvumernoi oblasti”, Probl. mat. analiza, 77, 2014, 55–61

[6] Temam R., Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981 | MR

[7] Dubinskii Yu. A., “Some coercive problems for the system of Poisson equations”, Russ. J. Math. Phys., 20:4 (2013), 402–412 | DOI | MR | Zbl