C^1,α estimates for the parallel refractor

2016/03/20 by Farhan Abedin, Abedin, Farhan, Cristian E. Gutiérrez +3
Computer Science · Mathematics · #35J96 #35Q60 #74J25 #78A05 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optics (physics.optics)

paper · pdf · doi:10.48550/arxiv.1603.06167

openalex publication_date 2016/03/20 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

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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