TY - JOUR
T1 - Hadamard's Fundamental Solution and Conical Refraction
JO - Journal of Partial Differential Equations
VL - 3
SP - 264
EP - 278
PY - 2000
DA - 2000/08
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5513.html
KW - Conic refraction
KW - Hadamard fundamental solution
KW - geometric-optical asymptotics
KW - boundary-layer type singularity
AB -  Conical refraction in anisotropic media shows two different light speeds, hence the charaderistic conoid is composed of two sheets. In a special case that two of the dielectric constants are equal, conic refraction is depicted by a partial differential operator which is factorizable. Thus the singular support of the fundamental solution should also be composed of two sheets. In this paper, the author gives the Hadamard construction of the fundamental solution which is just singular on these two sheets. In case of conic refraction considered, these two sheets are tangent to each other along two bi-characteristic curves, and a special singularity of the boundary-layer type appears there.