On the reflector shape design

Aram Karakhanyan The Australian National University Xu-Jia Wang Australian National University

Differential Geometry mathscidoc:1609.10173

Journal of Differential Geometry, 84, (3), 561-610, 2010
In this paper we study the problem of recovering the reflecting surface in a reflector system which consists of a point light source, a reflecting surface, and an object to be illuminated. This problem involves a fully nonlinear partial differential equation of MongeAmp`ere type, subject to a nonlinear second boundary condition. A weak solution can be obtained by approximation by piecewise ellipsoidal surfaces. The regularity is a very complicated issue but we found precise conditions for it.
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@inproceedings{aram2010on,
  title={ON THE REFLECTOR SHAPE DESIGN},
  author={Aram Karakhanyan, and Xu-Jia Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911213953162091830},
  booktitle={Journal of Differential Geometry},
  volume={84},
  number={3},
  pages={561-610},
  year={2010},
}
Aram Karakhanyan, and Xu-Jia Wang. ON THE REFLECTOR SHAPE DESIGN. 2010. Vol. 84. In Journal of Differential Geometry. pp.561-610. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911213953162091830.
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