Double layer potentials on three-dimensional wedges and pseudodifferential operators on Lie groupoids

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Qiao, Yu¹ 

[1] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710119, Shaanxi, Peoples R China

关键词: The method of layer potentials;    Double layer potential operator;    Convolution integral operator;    Pseudodifferential operator;    Groupoid C*-algebra;    Weighted Sobolev space;   

DOI  :  10.1016/j.jmaa.2018.01.077

来源: Elsevier

【 摘 要 】

Let W be a three-dimensional wedge, and K he the double layer potential operator associated to W and the Laplacian. We show that 1/2 +/- 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 C*(g)circle times M-2(C), where g is the action (transformation) groupoid M (sic) G, with G = {(1 0 a b) : a is an element of R, b is an element of R+}, which is a Lie group, and M is a kind of compactification of G. This result can be used to prove the Fredholmness of 1/2 + K-Omega, where Omega is a domain with edge singularities and K-Omega the double layer potential operator associated to the Laplacian and Omega. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free