Opuscula Math. 39, no. 1 (2019), 109-124
https://doi.org/10.7494/OpMath.2019.39.1.109

Opuscula Mathematica

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

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.

Mathematics Subject Classification: 35S15, 45A05.

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• Communicated by Marek Galewski.
• Revised: 2018-02-20.
• Accepted: 2018-02-21.
• Published online: 2018-08-07.