Volume 13, Issue 3
Hadamard's Fundamental Solution and Conical Refraction

Minyou Qi

DOI:

J. Part. Diff. Eq., 13 (2000), pp. 264-278.

Published online: 2000-08

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  • Abstract

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.

  • Keywords

Conic refraction Hadamard fundamental solution geometric-optical asymptotics boundary-layer type singularity

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@Article{JPDE-13-264, author = {}, title = {Hadamard's Fundamental Solution and Conical Refraction}, journal = {Journal of Partial Differential Equations}, year = {2000}, volume = {13}, number = {3}, pages = {264--278}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5513.html} }
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://dor.org/ UR - https://global-sci.org/intro/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.
Minyou Qi . (2019). Hadamard's Fundamental Solution and Conical Refraction. Journal of Partial Differential Equations. 13 (3). 264-278. doi:
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