Regularity for the near field parallel refractor and reflector problems

2014/04/15 by Cristian E. Gutierrez, Gutierrez, Cristian E., Federico Tournier +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1404.4011

32 pages, three figures

arxiv created 2014/04/15 · arxiv updated 2014/04/16

Abstract

We prove local C^1,α estimates of solutions for the parallel refractor and reflector problems under local assumptions on the target set Σ, and no assumptions are made on the smoothness of the densities.

Related

• C^1,α-estimates for the near field refractor
• C^1,α estimates for the parallel refractor
• Refractor surfaces determined by near-field data
• Pointwise estimates and regularity in geometric optics and other\n Generated Jacobian Equations
• Weak solutions to the near-field reflector problem with spatial restrictions approached with generalized reflectors constructed from ellipsoids