2015/01/28 by Nestor Guillen, Guillen, Nestor, Jun Kitagawa +1
Mathematics · Physics and Astronomy · #35B65 #35J96 #78A05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1501.07332
openalex publication_date 2015/01/28 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
The study of reflector surfaces in geometric optics necessitates the analysis\nof certain nonlinear equations of Monge-Amp `ere type known as generated\nJacobian equations. These equations, whose general existence theory has been\nrecently developed by Trudinger go beyond the framework of optimal transport.\nWe obtain pointwise estimates for weak solutions of such equations under a\ncondition analogous to the A3w condition of Ma, Trudinger and Wang. Estimates\nof this type have played an important role in the regularity theory for optimal\ntransport maps and were previously unknown in this context, including the\nimportant case of the near field reflector problem.\n