Boundary-value problems for analytic functions. Applications of complex analysis in some problems of continuum mechanics. Analytic solution of heterogeneous media problems with evaluation effective parameters.
Main publications:
Obnosov Yu.V., “Exact solution of a problem of R-linear conjugation for a rectangular checkerboard field”, Proceedings Royal Society London, A,, 452 (1996), 2423-2442
Obnosov Yu.V., “Periodic heterogeneous structures: new explicit solutions and effective characteristics of refraction of an imposed field”, SIAM J. Appl. Math., 59:4 (1999), 1267-1287
Yu. V. Obnosov, M. A. Egorova, “$\mathbb R$-linear conjugation problem for a confocal parabolic annulus”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 151:3 (2009), 170–178
A. M. Mal'tseva, Yu. V. Obnosov, S. V. Rogozin, “A generalization of Milne-Thomson theorem for the case of annulus”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 148:4 (2006), 35–50
Yu. V. Obnosov, “Solution of a problem of a seepage fields distribution into infinite porous massif with two circular inclusions”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 148:2 (2006), 109–123
I. R. Kayumov, Yu. V. Obnosov, “Estimates for integral means of hyperbolically convex functions”, Sibirsk. Mat. Zh., 46:6 (2005), 1316–1323; Siberian Math. J., 46:6 (2005), 1062–1068
2004
6.
Yu. V. Obnosov, “Solution of the $\mathbb R$-linear conjugation problem in the case of a hyperbolic line of separation of heterogeneous phases”, Izv. Vyssh. Uchebn. Zaved. Mat., 2004, no. 7, 53–62; Russian Math. (Iz. VUZ), 48:7 (2004), 50–59
A. R. Kasimov, Yu. V. Obnosov, “Exact values of efficiency for Muskat well arrays”, Dokl. Akad. Nauk, 353:2 (1997), 193–195
1996
8.
Yu. V. Obnosov, “Solution of the $\mathbf R$-linear conjugation problem in the theory of composites for a three-component medium”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, no. 5, 63–72; Russian Math. (Iz. VUZ), 40:5 (1996), 61–70
Yu. P. Iemets, Yu. V. Obnosov, Yu. P. Onofrychuk, “Electric forces in a dielectric two-layer cylinder with nonconcentric arrangement of layers”, Prikl. Mekh. Tekh. Fiz., 37:1 (1996), 3–14; J. Appl. Mech. Tech. Phys., 37:1 (1996), 1–11
Yu. V. Obnosov, “Closed solution of a problem of $R$-linear conjugation for a regular triangular checkerboard field”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, no. 8, 55–66; Russian Math. (Iz. VUZ), 38:8 (1994), 53–64
1993
11.
Yu. P. Iemets, Yu. V. Obnosov, Yu. P. Onofrychuk, “Electric forces on a circular cylindrical inclusion at the surface separating two dielectrics”, Prikl. Mekh. Tekh. Fiz., 34:4 (1993), 14–24; J. Appl. Mech. Tech. Phys., 34:4 (1993), 465–473
1992
12.
Yu. V. Obnosov, “Solution of a problem of $\mathbf{R}$-linear conjugation for a regular triangular chess field”, Dokl. Akad. Nauk, 327:3 (1992), 326–330; Dokl. Math., 37:11 (1992), 546–548
13.
Yu. V. Obnosov, “Solution of a boundary value problem of $\mathbb R$-linear conjugation with piecewise-constant coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, no. 4, 39–48; Russian Math. (Iz. VUZ), 36:4 (1992), 35–37
1991
14.
Yu. V. Obnosov, “Solution of a problem of Markushevich in a class of doubly
periodic functions with orthogonal periods”, Dokl. Akad. Nauk SSSR, 319:5 (1991), 1125–1127; Dokl. Math., 36:8 (1991), 573–574
1990
15.
Yu. P. Iemets, Yu. V. Obnosov, “An accurately solvable problem of the mutual effect of inclusions in the theory of heterogeneous media”, Prikl. Mekh. Tekh. Fiz., 31:1 (1990), 21–29; J. Appl. Mech. Tech. Phys., 31:1 (1990), 21–28
Yu. P. Iemets, Yu. V. Obnosov, “Exact solution of a problem on current formation in a doubly
periodic heterogeneous system”, Dokl. Akad. Nauk SSSR, 309:2 (1989), 319–322; Dokl. Math., 34:11 (1989), 972–974
Yu. V. Obnosov, “Solution of a mixed boundary value problem of the theory of analytic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1981, no. 10, 73–75
1979
19.
Yu. V. Obnosov, “On the solution of the linear Hilbert problem in a special case”, Izv. Vyssh. Uchebn. Zaved. Mat., 1979, no. 9, 29–40; Soviet Math. (Iz. VUZ), 23:9 (1979), 28–39
1978
20.
Yu. V. Obnosov, “The solution of the homogeneous Hilbert power problem with constant coefficient”, Trudy Sem. Kraev. Zadacham, 15 (1978), 99–107
1975
21.
Yu. V. Obnosov, “Solution of a certain nonlinear mixed boundary value problem of analytic function theory”, Izv. Vyssh. Uchebn. Zaved. Mat., 1975, no. 6, 96–102; Soviet Math. (Iz. VUZ), 19:6 (1975), 78–83
22.
Yu. V. Obnosov, “On the solution of a nonlinear boundary value problem of Hilbert type. II”, Izv. Vyssh. Uchebn. Zaved. Mat., 1975, no. 4, 42–51; Soviet Math. (Iz. VUZ), 19:4 (1975), 33–39
23.
Yu. V. Obnosov, “On the solution of a nonlinear boundary value problem of Hilbert type. I”, Izv. Vyssh. Uchebn. Zaved. Mat., 1975, no. 3, 82–91; Soviet Math. (Iz. VUZ), 19:3 (1975), 64–71
1973
24.
Yu. V. Obnosov, “A nonlinear boundary value problem of Hilbert type”, Izv. Vyssh. Uchebn. Zaved. Mat., 1973, no. 10, 42–49
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