Abstract
We introduce a model to design reflectors that take into account the inverse square law for radiation. We prove existence of solutions in the near field case when the input and output energies are prescribed.
Al diletto amico Ermanno Lanconelli in occasione del suo settantesimo compleanno
AMS Subject Classification: 78A05, 35J96, 35Q60
Dedicated to Ermanno Lanconelli on the occasion of his 70th birthday.
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Notes
- 1.
The units for this quantity are Watts because the units for \(\varOmega \subseteq S^{2}\) are considered non dimensional units, i.e., \(\varOmega\) is measured in steradians.
- 2.
From [11, Theorem (11.5)] every Borel subset of X is Carathéodory measurable.
- 3.
For a, b vectors in \(\mathbb{R}^{3}\), a ⊗ b is the matrix a t b.
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Gutiérrez, C.E., Sabra, A. (2015). The Reflector Problem and the Inverse Square Law. In: Citti, G., Manfredini, M., Morbidelli, D., Polidoro, S., Uguzzoni, F. (eds) Geometric Methods in PDE’s. Springer INdAM Series, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-02666-4_15
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DOI: https://doi.org/10.1007/978-3-319-02666-4_15
Publisher Name: Springer, Cham
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