The Parallel Refractor

Gutiérrez, Cristian E.; Tournier, Federico

doi:10.1007/978-1-4614-4075-8_14

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Introduction4

Theorem 931

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Cited by 13 publications

(25 citation statements)

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“…Existence of solutions with this definition of parallel reflector can be proved in a way similar to the existence of parallel refractors as done in [5]. We omit the corresponding details.…”

Section: Theorem 93mentioning

confidence: 98%

See 1 more Smart Citation

Regularity for the near field parallel refractor and reflector problems

Gutiérrez

Tournier

2014

Calc. Var.

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“…Existence of solutions with this definition of parallel reflector can be proved in a way similar to the existence of parallel refractors as done in [5]. We omit the corresponding details.…”

Section: Theorem 93mentioning

confidence: 98%

“…Under general conditions on and , and when σ is a Radon measure in D, the existence of parallel refractors is proved in [5].…”

Section: Introductionmentioning

confidence: 98%

Regularity for the near field parallel refractor and reflector problems

Gutiérrez

Tournier

2014

Calc. Var.

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“…When medium II is denser than medium I (i.e. n 1 < n 2 ), C 1,α estimates are proved in [GT15], and the existence of refractors is proved in [GT13]. The purpose of this paper is to consider the case when n 1 > n 2 .…”

Section: Introductionmentioning

confidence: 99%

C1,α estimates for the parallel refractor

2016

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We consider the parallel refractor problem when the planar radiating source lies in a medium having higher refractive index than the medium in which the target is located. We prove local C 1,α estimates for parallel refractors under suitable geometric assumptions on the source and target, and under local regularity hypotheses on the target set. We also discuss existence of refractors under energy conservation assumptions.

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“…Illumination problems with one point source are studied in [GH14], [GM13] for the refraction case and in [CKO99], [Wan96], [KO97], [GS14b] for reflection. The case when the input rays are collimated is considered in [GT13], [GT14]. March 7, 2016.…”

Section: Introductionmentioning

confidence: 99%