Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail: Keywords: ill-posed Cauchy Problem,
operators with injective symbol,
Carleman's formula,
differential complexes. non-coercive mixed problems for elliptic equations,
completeness of root functions,
mixed problems for parabolic equations.
UDC: 517.55, 517.575, 517.95, 517.955, 517.956, 517.98, 517.983, 517.956.4
Subject:
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
