We develop an enclosure-type reconstruction scheme to identify penetrable and impenetrable obstacles in an electromagnetic field with anisotropic medium in ℝ3. The main difficulty in treating this problem lies in the fact that there are so far no complex geometrical optics solutions available for Maxwell's equation with anisotropic medium in ℝ3. Instead, we derive and use another type of special solutions called oscillating-decaying solutions. To justify this scheme, we use Meyers- Lp estimate, for the Maxwell system, to compare the integrals coming from oscillating-decaying solutions and those from the reflected solutions.
- Enclosure method
- Meyers L estimates
- Oscillating-decaying solutions
- Runge approximation property