C1, α estimates for the parallel refractor. (September 2016)

• Record Type: Journal Article
• Authors: Abedin, Farhan; Gutiérrez, Cristian E.; Tralli, Giulio
• Is Part Of: Nonlinear analysis. Volume 142(2016)
• Page Start: 1
• Page End: 25
• Publication Date: 2016-09
• Subjects: Analysis of pdes -- Geometric optics -- Holder estimates; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.04.001
• Languages: English
• ISSNs: 0362-546X

Abstract

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.