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Pseudo-differential equations and conical potentials: 2-dimensional case

Vasilyev Vladimir B.

Opuscula Mathematica

2019

Vol. 39, no. 1

109--124

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.