@article{ChelkhLyTarkhanov2020,
  author    = {Chelkh, W. and Ly, Ibrahim and Tarkhanov, Nikolai},
  title     = {A remark on the Laplace transform},
  series = {Siberian Mathematical Journal},
  volume    = {61},
  journal   = {Siberian Mathematical Journal},
  number    = {4},
  publisher = {Consultants Bureau, Springer},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446620040151},
  pages     = {755 -- 762},
  year      = {2020},
  abstract  = {The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.},
  language  = {en}
}
@phdthesis{Ly2009,
  author    = {Ly, Ibrahim},
  title     = {Asymptotic solutions of the Cauchy problem for nonlinear elliptic differential equations},
  address   = {Potsdam},
  pages     = {VI, 100 S.},
  year      = {2009},
  language  = {en}
}
@article{Ly2020,
  author    = {Ly, Ibrahim},
  title     = {A Cauchy problem for the Cauchy-Riemann operator},
  series = {Afrika Matematika},
  volume    = {32},
  journal   = {Afrika Matematika},
  number    = {1-2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1012-9405},
  doi       = {10.1007/s13370-020-00810-4},
  pages     = {69 -- 76},
  year      = {2020},
  abstract  = {We study the Cauchy problem for a nonlinear elliptic equation with data on a piece S of the boundary surface partial derivative X. By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain X with the property that the data on S, if combined with the differential equations in X, allows one to determine all derivatives of u on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.},
  language  = {en}
}
@unpublished{LyTarkhanov2013,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {Generalised Beltrami equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67416},
  year      = {2013},
  abstract  = {We enlarge the class of Beltrami equations by developping a stability theory for the sheaf of solutions of an overdetermined elliptic system of first order homogeneous partial differential equations with constant coefficients in the Euclidean space.},
  language  = {en}
}
@unpublished{LyTarkhanov2015,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rad{\´o} theorem for p-harmonic functions},
  volume    = {4},
  number    = {3},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-71492},
  pages     = {10},
  year      = {2015},
  abstract  = {Let A be a nonlinear differential operator on an open set X in 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 the complement of S 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.},
  language  = {en}
}
@unpublished{LyTarkhanov2015,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {Asymptotic expansions at nonsymmetric cuspidal points},
  volume    = {4},
  number    = {7},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78199},
  pages     = {11},
  year      = {2015},
  abstract  = {We study asymptotics of solutions to the Dirichlet problem in a domain whose boundary contains a nonsymmetric conical point. We establish a complete asymptotic expansion of solutions near the singular point.},
  language  = {en}
}
@article{LyTarkhanov2016,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rado theorem for p-harmonic functions},
  series = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana},
  volume    = {22},
  journal   = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1405-213X},
  doi       = {10.1007/s40590-016-0109-7},
  pages     = {461 -- 472},
  year      = {2016},
  abstract  = {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.},
  language  = {en}
}
@article{LyTarkhanov2015,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {Generalized Beltrami equations},
  series = {Complex variables and elliptic equations},
  volume    = {60},
  journal   = {Complex variables and elliptic equations},
  number    = {1},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2013.876759},
  pages     = {24 -- 37},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@article{LyTarkhanov2020,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolaj Nikolaevič},
  title     = {Asymptotic expansions at nonsymmetric cuspidal points},
  series = {Mathematical notes},
  volume    = {108},
  journal   = {Mathematical notes},
  number    = {1-2},
  publisher = {Springer Science},
  address   = {New York},
  issn      = {0001-4346},
  doi       = {10.1134/S0001434620070238},
  pages     = {219 -- 228},
  year      = {2020},
  abstract  = {We study the asymptotics of solutions to the Dirichlet problem in a domain X subset of R3 whose boundary contains a singular point O. In a small neighborhood of this point, the domain has the form {z > root x(2) + y(4)}, i.e., the origin is a nonsymmetric conical point at the boundary. So far, the behavior of solutions to elliptic boundary-value problems has not been studied sufficiently in the case of nonsymmetric singular points. This problem was posed by V.A. Kondrat'ev in 2000. We establish a complete asymptotic expansion of solutions near the singular point.},
  language  = {en}
}