Reularizagtion of the ill-posed Cauchy problem for elliptic systems and complexes;
acyclicity of differential complexes;
boundary value problems for elliptic systems
(the Cauchy problem, Dirichlet problem, mixed problems);
duality in spaces of solutions to elliptic systems;
completeness of the root functions of non-coercive mixed problems for elliptic equations in
the Sobolev–Slobodetskii spaces;
boundary problems for parabolic equations.
Main publications:
Shlapunov A., Tarkhanov N., “On completeness of root functions
of Sturm–Liouville problems
with discontinuous boundary operators”, Journal of Differential Equations, 255 (2013), 3302–3335
Shlapunov A., Tarkhanov N., “Mixed problems with a parameter”, Russian J. Math. Phys., 12:1 (2005), 97–124
Schulze B.-W., Shlapunov A. Tarkhanov N., “Green integrals on manifolds with cracks”, Annals of Global Analysis and Geometry, 24 (2003), 131–160
Shlapunov A., Tarkhanov N., “Duality by reproducing kernels”, International Journal of Math. and Math. Sciences, 2003:6 (2003), 1–78
Shlapunov A., Tarkhanov N., “Bases with double orthogonality in the Cauchy problem for systems with injective symbols”, The Proceedings of the London Mathematical Society, 71:1 (1995), 1–52
K. V. Gagelgans, A. A. Shlapunov, “On the de Rham complex on a scale of anisotropic weighted Hölder spaces”, Sib. Èlektron. Mat. Izv., 17 (2020), 428–444
2019
2.
Ilya A. Kurilenko, Alexander A. Shlapunov, “On Carleman-type formulas for solutions to the heat equation”, J. Sib. Fed. Univ. Math. Phys., 12:4 (2019), 421–433
3.
Azal Mera, Alexander A. Shlapunov, Nikolai Tarkhanov, “Navier–Stokes equations for elliptic complexes”, J. Sib. Fed. Univ. Math. Phys., 12:1 (2019), 3–27
4.
K. V. Sidorova (Gagelgans), A. A. Shlapunov, “On the Closure of Smooth Compactly Supported Functions in Weighted Hölder Spaces”, Mat. Zametki, 105:4 (2019), 616–631; Math. Notes, 105:4 (2019), 604–617
2018
5.
Andrei A. Parfenov, Alexander A. Shlapunov, “On the Fredholm property for the steady Navier–Stokes equations in weighted Hölder spaces”, J. Sib. Fed. Univ. Math. Phys., 11:5 (2018), 659–662
2017
6.
A. N. Polkovnikov, A. A. Shlapunov, “Construction of Carleman formulas by using mixed problems with parameter-dependent boundary conditions”, Sibirsk. Mat. Zh., 58:4 (2017), 870–884; Siberian Math. J., 58:4 (2017), 676–686
2016
7.
Yulia L. Cherepanova, Alexander A. Shlapunov, “On an analogue of the Riemann–Hilbert problem for a non-linear perturbation of the Cauchy–Riemann operator”, J. Sib. Fed. Univ. Math. Phys., 9:4 (2016), 427–431
2015
8.
N. Tarkhanov, A. A. Shlapunov, “Sturm–Liouville problems in weighted spaces in domains with nonsmooth edges. II”, Mat. Tr., 18:2 (2015), 133–204; Siberian Adv. Math., 26:4 (2016), 247–293
9.
N. Tarkhanov, A. A. Shlapunov, “Sturm–Liouville problems in weighted spaces in domains with nonsmooth edges. I”, Mat. Tr., 18:1 (2015), 118–189; Siberian Adv. Math., 26:1 (2016), 30–76
2013
10.
Alexander N. Polkovnikov, Aleksander A. Shlapunov, “On the spectral properties of a non-coercive mixed problem associated with $\overline\partial$-operator”, J. Sib. Fed. Univ. Math. Phys., 6:2 (2013), 247–261
2012
11.
Roman E. Puzyrev, Alexander A. Shlapunov, “On an ill-posed problem for the heat equation”, J. Sib. Fed. Univ. Math. Phys., 5:3 (2012), 337–348
2011
12.
Alexander A. Shlapunov, “Boundary problems for Helmholtz equation and the Cauchy problem for Dirac operators”, J. Sib. Fed. Univ. Math. Phys., 4:2 (2011), 217–228
2009
13.
Ivan V. Shestakov, Alexander A. Shlapunov, “Negative Sobolev Spaces in the Cauchy Problem for the Cauchy–Riemann Operator”, J. Sib. Fed. Univ. Math. Phys., 2:1 (2009), 17–30
14.
I. V. Shestakov, A. A. Shlapunov, “The Cauchy problem for operators with injective symbol in the Lebesgue space $L^2$ in a domain”, Sibirsk. Mat. Zh., 50:3 (2009), 687–702; Siberian Math. J., 50:3 (2009), 547–559
2008
15.
Ivan V. Shestakov, Alexander A. Shlapunov, “On the Cauchy Problem for Operators with Injective Symbols in Sobolev Spaces”, J. Sib. Fed. Univ. Math. Phys., 1:1 (2008), 52–62
16.
D. P. Fedchenko, A. A. Shlapunov, “On the Cauchy problem for the multi-dimensional Cauchy-Riemann operator in the Lebesgue space $L^2$ in a domain”, Mat. Sb., 199:11 (2008), 141–160; Sb. Math., 199:11 (2008), 1715–1733
2006
17.
N. N. Tarkhanov, A. A. Shlapunov, “Green's formulas in complex analysis”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 108 (2006), 106–157; J. Math. Sci. (N. Y.), 120:6 (2004), 1868–1900
18.
A. A. Shlapunov, “A Method for Constructing Solutions to Linear Systems of Partial Differential Equations”, Mat. Tr., 9:2 (2006), 191–204; Siberian Adv. Math., 17:2 (2007), 144–152
2005
19.
A. A. Shlapunov, “On some conditions for the solvability of overdetermined systems of differential equations in Sobolev spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, 4, 70–80; Russian Math. (Iz. VUZ), 49:4 (2005), 67–76
2002
20.
A. A. Shlapunov, “On duality in spaces of polyharmonic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2002, 8, 79–81; Russian Math. (Iz. VUZ), 46:8 (2002), 75–77
21.
A. A. Shlapunov, “On duality in spaces of solutions to elliptic systems”, Sibirsk. Mat. Zh., 43:4 (2002), 953–963; Siberian Math. J., 43:4 (2002), 769–777
2001
22.
A. A. Shlapunov, “On a olvability condition for systems with an injective symbol in terms of iterations of double layer potentials”, Sibirsk. Mat. Zh., 42:4 (2001), 952–963; Siberian Math. J., 42:4 (2001), 801–810
1994
23.
L. A. Aizenberg, O. V. Karepov, A. A. Shlapunov, “On the property of uniqueness and existence of a limit in Carleman's formulas”, Trudy Mat. Inst. Steklov., 203 (1994), 3–12; Proc. Steklov Inst. Math., 203 (1995), 1–9
1992
24.
N. N. Tarkhanov, A. A. Shlapunov, “Bases with double orthogonality in the Cauchy problem for systems
with an injective symbol”, Dokl. Akad. Nauk, 326:1 (1992), 45–49; Dokl. Math., 46:2 (1993), 225–230
25.
A. A. Shlapunov, N. N. Tarkhanov, “On the Cauchy problem for holomorphic functions of the Lebesgue class $L^2$ in a domain”, Sibirsk. Mat. Zh., 33:5 (1992), 186–195; Siberian Math. J., 33:5 (1992), 914–922
26.
A. A. Shlapunov, “On the Cauchy problem for the Laplace equation”, Sibirsk. Mat. Zh., 33:3 (1992), 205–215; Siberian Math. J., 33:3 (1992), 534–542
Full list of publications
