Kutaiba, Shaban H.; Vasilyev, Vladimir B. On limit behavior of a solution to boundary value problem in a plane sector. (English) Zbl 1476.35351 Math. Methods Appl. Sci. 44, No. 15, 11904-11912 (2021). Summary: We study a certain boundary value problem in Sobolev-Slobodetskii spaces with integral condition in a plane excluding a ray from origin. Using auxiliary problem in outside of a convex cone and the wave factorization concept, we construct a general solution and consider transfer to limit boundary value problem. It was shown that limit boundary value problem can be solvable only if the boundary function satisfies to a certain singular functional equation. Cited in 1 Document MSC: 35S15 Boundary value problems for PDEs with pseudodifferential operators 47G30 Pseudodifferential operators Keywords:elliptic pseudo-differential equation; limit boundary value problem; wave factorization; general solution PDFBibTeX XMLCite \textit{S. H. Kutaiba} and \textit{V. B. Vasilyev}, Math. Methods Appl. Sci. 44, No. 15, 11904--11912 (2021; Zbl 1476.35351) Full Text: DOI Link