Abstract
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 Monge- Ampère 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.
| Original language | English |
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| Pages (from-to) | 561-610 |
| Journal | Journal of Differential Geometry |
| Volume | 84 |
| Issue number | 3 |
| Publication status | Published - 2010 |