Enclosure methods to some PDEs (2)
林奕亘先生國立台灣大學數學系 下午 1:00–3:00 健雄館 208室We develop an enclosure-type method to identify penetrable and impenetrable obstacles in some anisotropic medium in R^3. The main difficulty in treating this problem lies in the fact that there are so far no complex geometrical opticssolutions available for the PDEs. Instead, we derive and use another type special solutions called the oscillating-decaying solutions. To justify the scheme, we can use the Meyers' L^p estimates for such PDEs, to compare the integrals coming from oscillating-decayingsolutions and those from the reflected solutions.