ABOUT ONE PSEUDODIFFERENTIAL PROBLEM

Abstract

Abstract: One problem is considered, which belongs to the theory of pseudodifferential operators (abbreviated as PDO). The theory of PDO has developed from the theory of singular integral operators. In its modern form, it was created in the mid-60s of the twentieth century. Therefore, it is natural that one of the most significant areas of application of PDOs are problems associated with singular operators. The considered problem is studied using the methods of the theory of variational inequalities. Existence, uniqueness, and well-posedness theorems for the solutions of the considered variational inequalities are proved.