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 Rado theorem for the porous medium equation
JF  - Boletin de la Sociedad Matemática Mexicana
N2  - We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi.
KW  - Quasilinear equations
KW  - Removable sets
KW  - Porous medium equation
Y1  - 2017
U6  - https://doi.org/10.1007/s40590-017-0169-3
SN  - 1405-213X
SN  - 2296-4495
VL  - 24
IS  - 2
SP  - 427
EP  - 437
PB  - Springer
CY  - Cham
ER  - 
TY  - JOUR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Rado theorem for p-harmonic functions
JF  - Boletin de la Sociedad Matemática Mexicana
N2  - Let A be a nonlinear differential operator on an open set X subset of R-n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in XS of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A.
KW  - Quasilinear equations
KW  - Removable sets
KW  - p-Laplace equation
Y1  - 2016
U6  - https://doi.org/10.1007/s40590-016-0109-7
SN  - 1405-213X
SN  - 2296-4495
VL  - 22
SP  - 461
EP  - 472
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Makhmudov, K. O.
A1  - Makhmudov, O. I.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A nonstandard Cauchy problem for the heat equation
JF  - Mathematical Notes
N2  - We consider the Cauchy problem for the heat equation in a cylinder C (T) = X x (0, T) over a domain X in R (n) , with data on a strip lying on the lateral surface. The strip is of the form S x (0, T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S, we derive an explicit formula for solutions of this problem.
Y1  - 2017
U6  - https://doi.org/10.1134/S0001434617070264
SN  - 0001-4346
SN  - 1573-8876
VL  - 102
SP  - 250
EP  - 260
PB  - Pleiades Publ.
CY  - New York
ER  - 
TY  - JOUR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A general index formula on toric manifolds with conical point
Y1  - 2001
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  -