Geodesic
Non-linear analytic and coanalytic problems ($L_p$-theory, Clifford analysis, examples)
Sbornik. Mathematics, Tome 191 (2000) no. 1, pp. 61-95 
Yu. A. Dubinskii; A. S. Osipenko. Non-linear analytic and coanalytic problems ($L_p$-theory, Clifford analysis, examples). Sbornik. Mathematics, Tome 191 (2000) no. 1, pp. 61-95. http://geodesic.mathdoc.fr/item/SM_2000_191_1_a2/
@article{SM_2000_191_1_a2,
     author = {Yu. A. Dubinskii and A. S. Osipenko},
     title = {Non-linear analytic and coanalytic problems ($L_p$-theory, {Clifford} analysis, examples)},
     journal = {Sbornik. Mathematics},
     pages = {61--95},
     year = {2000},
     volume = {191},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_1_a2/}
}
TY  - JOUR
AU  - Yu. A. Dubinskii
AU  - A. S. Osipenko
TI  - Non-linear analytic and coanalytic problems ($L_p$-theory, Clifford analysis, examples)
JO  - Sbornik. Mathematics
PY  - 2000
SP  - 61
EP  - 95
VL  - 191
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_2000_191_1_a2/
LA  - en
ID  - SM_2000_191_1_a2
ER  - 
%0 Journal Article
%A Yu. A. Dubinskii
%A A. S. Osipenko
%T Non-linear analytic and coanalytic problems ($L_p$-theory, Clifford analysis, examples)
%J Sbornik. Mathematics
%D 2000
%P 61-95
%V 191
%N 1
%U http://geodesic.mathdoc.fr/item/SM_2000_191_1_a2/
%G en
%F SM_2000_191_1_a2

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

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the “orthogonal” sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

[1] Dubinskii Yu. A., “Ob analiticheskikh “kraevykh” zadachakh na ploskosti”, UMN, 52:3 (1997), 53–104 | MR | Zbl

[2] Dubinskii Yu. A., “Ob analiticheskoi nelineinoi periodicheskoi zadache”, Differents. uravneniya, 29:3 (1993), 371–381 | MR

[3] Dubinskii Yu. A., “O nekotorykh ortogonalnykh razlozheniyakh i nelineinoi analiticheskoi zadache”, Differents. uravneniya, 31:2 (1995), 262–275 | MR

[4] Colombeau J. F., Elementary introduction to new generalized functions, North-Holland, Amsterdam, 1985 | MR | Zbl

[5] Egorov Yu. V., “K teorii obobschennykh funktsii”, UMN, 45:5 (1990), 3–40 | MR | Zbl

[6] Livchak Ya. B., “K teorii obobschennykh funktsii”, Trudy Rizhskogo algebraicheskogo seminara, 1969, 98–164

[7] Antonevich A. B., Radyno Ya. V., “Ob obschem metode postroeniya algebr obobschennykh funktsii”, Dokl. AN SSSR, 318:5 (1991), 267–270 | MR | Zbl

[8] Oberhuggenberger M., “Multiplication of distributions in the Colombeau algebra”, Bulletino U.M.1, 5.a:6 (1986), 423–429 | MR

[9] Roitberg Ya. A., Ellipticheskie granichnye zadachi v obobschennykh funktsiyakh, Preprint I–IV, Izd-vo pedagogicheskogo instituta, Chernigov, 1990

[10] Dubinskii Yu. A., Osipenko A. S., “Ob analiticheskoi nelineinoi zadache v polose”, Vestnik MEI, 1995, no. 6, 29–40

[11] Zubkov P. V., “Analiticheskaya nelineinaya variatsionnaya zadacha v prostranstvakh s vesom”, Vestnik MEI, 1995, no. 6, 57–70

[12] Dubinskii Yu. A., “O prodolzhenii funktsii s naimenshim koanaliticheskim ukloneniem”, Matem. zametki, 64:1 (1998), 45–57 | MR | Zbl

[13] Dubinskii Yu. A., “Ob odnoi zadache nailuchshego prodolzheniya periodicheskoi funktsii”, Dokl. AN, 360:1 (1998), 10–12 | MR | Zbl

[14] Osipenko A. S., “Nelineinaya analiticheskaya zadacha variatsionnogo tipa v prostranstvakh $W_p^m$ v polose”, Vestnik MEI, 1997, no. 6, 78–88 | MR

[15] Dubinskii Yu. A., Osipenko A. S., “$L_p$-teoriya nekotorykh analiticheskikh i koanaliticheskikh zadach variatsionnogo tipa”, Vestnik MEI, 1997, no. 6, 18–30

[16] Dubinskii Yu. A., Osipenko A. S., “Ob “ortogonalnom” razlozhenii sobolevskikh prostranstv v summu analiticheskikh i koanaliticheskikh podprostranstv”, Dokl. AN, 359:6 (1998), 735–738 | MR | Zbl

[17] Bari N. K., Trigonometricheskie ryady, Nauka, M., 1961 | MR

[18] Brackx F., Delanghe R., Sommen F., Clifford analysis, Pitman, Boston, 1982 | MR | Zbl