Solution of boundary problems for elliptic equation in domains with conical or corner points

Abstract

The paper focuses on solving boundary problems for elliptic equation in domains with conical or corner singular points. The solution is constructed in the special function spaces which have derivatives that sum with some weights. These function spaces catch the main feature of the solution to such problems: it is everywhere smooth, except for conical points. Generally speaking, these derivatives have power singularities when approaching the conical point. Study of the conical point range is the main objective when solving the boundary problem. To solve the problem the method proposed by V. A. Kondratiev [1] has been used. The proposed approach can be used to solve various diffraction problems. For example, it is suitable to study masking problems that require thorough analysis of the singular points of masking shells, which arise after application of certain coordinate transformations [2].