Opuscula Math. 39, no. 1 (2019), 109-124
Pseudo-differential equations and conical potentials: 2-dimensional case
Vladimir B. Vasilyev
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.