Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899870 | Journal of Mathematical Analysis and Applications | 2018 | 21 Pages |
Abstract
Let W be a three-dimensional wedge, and K be the double layer potential operator associated to W and the Laplacian. We show that 12±K are isomorphisms between suitable weighted Sobolev spaces, which implies a solvability result in weighted Sobolev spaces for the Dirichlet problem on W. Furthermore, we show that the double layer potential operator K is an element in Câ(G)âM2(C), where G is the action (transformation) groupoid MâG, with G={(10ab):aâR,bâR+}, which is a Lie group, and M is a kind of compactification of G. This result can be used to prove the Fredholmness of 12+KΩ, where Ω is “a domain with edge singularities” and KΩ the double layer potential operator associated to the Laplacian and Ω.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yu Qiao,