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Browsing by Subject "pseudo-differential equation"

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    Item type:Article, Access status: Open Access ,
    Pseudo-differential equations and conical potentials: 2-dimensional case
    (Wydawnictwa AGH, 2019) Vasilev, Vladimir Borisovič
    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.