具有非光滑边界的散射问题

Existence and uniqueness of solutions to scattering problem with non-smooth boundary

讨论了一类具有非光滑边界的散射体的散射问题.为了简单起见,只针对R2空间.通过单双层位势,所讨论的问题可以化为一个边界积分方程.由于边界不光滑(有尖点),必须对边界积分算子进行仔细分析,最后得到了相应解的存在性和唯一性.

This paper discusses the scattering problem with non-smooth boundary. For simplicity, the discussion will be restricted in R2 space. However the problem can be reformulated as a bounding integral equation by using the single, and double-layer potentials. The existence and uniqueness of the solution can be obtained by carefully analysis of the boundary integral operators（with singular point）.