TY  - JOUR
A1  - Bagderina, Yulia Yu.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Solution of the equivalence problem for the third Painleve equation
JF  - Journal of mathematical physics
N2  - We find necessary conditions for a second order ordinary differential equation to be equivalent to the Painleve III equation under a general point transformation. Their sufficiency is established by reduction to known results for the equations of the form y ' = f (x, y). We consider separately the generic case and the case of reducibility to an autonomous equation. The results are illustrated by the primary resonance equation.
Y1  - 2015
U6  - https://doi.org/10.1063/1.4905383
SN  - 0022-2488
SN  - 1089-7658
VL  - 56
IS  - 1
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Generalized Beltrami equations
JF  - Complex variables and elliptic equations
N2  - We enlarge the class of Beltrami equations by developing a stability theory for the sheaf of solutions of an overdetermined elliptic system of first-order homogeneous partial differential equations with constant coefficients in Rn.
KW  - quasiconformal mapping
KW  - Beltrami equation
Y1  - 2015
U6  - https://doi.org/10.1080/17476933.2013.876759
SN  - 1747-6933
SN  - 1747-6941
VL  - 60
IS  - 1
SP  - 24
EP  - 37
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - JOUR
A1  - Antoniouk, Alexandra Viktorivna
A1  - Kiselev, Oleg M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point
JF  - Ukrainian mathematical journal
N2  - The Dirichlet problem for the heat equation in a bounded domain aS, a"e (n+1) is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t = c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii's paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior.
Y1  - 2015
U6  - https://doi.org/10.1007/s11253-015-1038-8
SN  - 0041-5995
SN  - 1573-9376
VL  - 66
IS  - 10
SP  - 1455
EP  - 1474
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Fedchenko, Dmitri
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An index formula for Toeplitz operators
JF  - Complex variables and elliptic equations
N2  - We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first-order partial differential equations in a bounded domain in R-n with smooth boundary.
KW  - Toeplitz operators
KW  - Fredholm property
KW  - index
KW  - Primary: 47B35
KW  - Secondary: 47L80
Y1  - 2015
U6  - https://doi.org/10.1080/17476933.2015.1050007
SN  - 1747-6933
SN  - 1747-6941
VL  - 60
IS  - 12
SP  - 1764
EP  - 1787
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - JOUR
A1  - Fedchenko, Dmitry
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Class of Toeplitz Operators in Several Variables
JF  - Advances in applied Clifford algebras
N2  - We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.
KW  - Cauchy data spaces
KW  - Laplace-Beltrami operator
KW  - Toeplitz operators
KW  - Fredholm property
Y1  - 2015
U6  - https://doi.org/10.1007/s00006-015-0546-9
SN  - 0188-7009
SN  - 1661-4909
VL  - 25
IS  - 4
SP  - 811
EP  - 828
PB  - Springer
CY  - Basel
ER  -