On an Algebra of a Certain Class of Operators in a Slab Domain in R2

In this paper a Dirichlet problem for the Laplacian in a domain with a corner in R² is treated and a new method of construction of a local parametrix for that Dirichlet problem at a corner point is given. In order to construct a parametrix a certain class of operators in a slab domain is introduced and it is shown that that operator class is an algebra.