@Article{Vasilyev2019,
author = "Vasilyev, Vladimir B.",
title = "Pseudo-differential equations and conical potentials: 2-dimensional case",
journal = "Opuscula Math.",
year = "2019",
volume = "39",
number = "1",
pages = "109--124",
doi = "https://doi.org/10.7494/OpMath.2019.39.1.109",
url = "https://doi.org/10.7494/OpMath.2019.39.1.109",
abstract = "We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.",
keywords = "pseudo-differential equation, wave factorization, Dirichlet problem, system of linear integral equations",
issn = "1232-9274"
}