Geodesic
Decompositions of the Sobolev--Clifford Modules and Nonlinear Variational Problems
Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 57-74.

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

We establish a general direct decomposition of modules and then, using this decomposition, prove representations of the Sobolev–Clifford modules as the sums of submodules of monogenic and comonogenic functions. We also show how the decompositions obtained can be applied to solving Stokes-type nonlinear variational problems. 
@article{TRSPY_2008_260_a4,
     author = {I. A. Borovikov and Yu. A. Dubinskii},
     title = {Decompositions of the {Sobolev--Clifford} {Modules} and {Nonlinear} {Variational} {Problems}},
     journal = {Informatics and Automation},
     pages = {57--74},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a4/}
}
TY  - JOUR
AU  - I. A. Borovikov
AU  - Yu. A. Dubinskii
TI  - Decompositions of the Sobolev--Clifford Modules and Nonlinear Variational Problems
JO  - Informatics and Automation
PY  - 2008
SP  - 57
EP  - 74
VL  - 260
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a4/
LA  - ru
ID  - TRSPY_2008_260_a4
ER  - 
%0 Journal Article
%A I. A. Borovikov
%A Yu. A. Dubinskii
%T Decompositions of the Sobolev--Clifford Modules and Nonlinear Variational Problems
%J Informatics and Automation
%D 2008
%P 57-74
%V 260
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a4/
%G ru
%F TRSPY_2008_260_a4
I. A. Borovikov; Yu. A. Dubinskii. Decompositions of the Sobolev--Clifford Modules and Nonlinear Variational Problems. Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 57-74. http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a4/

[1] Borovikov I. A., “Nekotorye razlozheniya prostranstv S. L. Soboleva i ikh prilozheniya”, Vestn. MEI, 2005, no. 6, 25–41

[2] Gaevskii Kh., Grëger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[3] Dubinskii Yu. A., Osipenko A. S., “Nelineinye analiticheskie i koanaliticheskie zadachi ($L_p$-teoriya, kliffordov analiz, primery)”, Mat. sb., 191:1 (2000), 65–102 | MR | Zbl

[4] Dubinskii Yu. A., “Razlozheniya prostranstv $W_p^m$ i $D_p^{m,k}$ v summu solenoidalnykh i potentsialnykh podprostranstv i faktorizatsionnye neravenstva”, DAN, 408:2 (2006), 160–164 | MR

[5] Leng S., Algebra, Mir, M., 1968

[6] Roitberg Ya. A., Ellipticheskie granichnye zadachi v obobschennykh funktsiyakh, Pedinstitut, Chernigov, 1990

[7] Begehr H., Dubinskii Ju., “Orthogonal decompositions of Sobolev spaces in Clifford analysis”, Ann. Mat. Pura ed Appl. Ser. 4, 181:1 (2002), 55–71 | DOI | MR | Zbl

[8] Dubinskii Ju., Reissig M., “Variational problems in Clifford analysis”, Math. Meth. Appl. Sci., 25 (2002), 1161–1176 | DOI | MR | Zbl

[9] Roitberg Ya., Elliptic boundary value problems in the spaces of distributions, Math. and Appl., 384, Kluwer, Dordrecht, 1996 | MR | Zbl

[10] J. Ryan (ed.), Clifford algebras in analysis and related topics, CRC Press, Boca Raton, FL, 1996 | MR