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C. Gutiérrez, Federico Tournier (2014)
Regularity for the near field parallel refractor and reflector problemsCalculus of Variations and Partial Differential Equations, 54
F Abedin, CE Gutiérrez, G Tralli (2016)
$$C^{1,\alpha }$$ C 1 , α regularity for the parallel refractorNonlinear Anal., 142
C. Gutiérrez, Federico Tournier (2013)
The Parallel Refractor
L. Caffarelli, S. Kochengin (1999)
On the Numerical Solution of the Problem of Reflector Design with Given Far-Field Scattering Data
C. Gutiérrez, Qingbo Huang (2009)
The Refractor Problem in Reshaping Light BeamsArchive for Rational Mechanics and Analysis, 193
CE Gutiérrez, F Tournier (2015)
Regularity for the near field parallel refractor and reflector problemsCalc. Var. PDEs, 54
J Kitagawa (2014)
An iterative scheme for solving the optimal transportation problemCalc. Var. PDEs, 51
L. Evans (1992)
Measure theory and fine properties of functions
Xinwen Ma, N. Trudinger, Xu-jia Wang (2005)
Regularity of Potential Functions of the Optimal Transportation ProblemArchive for Rational Mechanics and Analysis, 177
N. Trudinger (2012)
On the local theory of prescribed Jacobian equationsDiscrete and Continuous Dynamical Systems, 34
G. Loeper (2009)
On the regularity of solutions of optimal transportation problemsActa Mathematica, 202
R Leo, CE Gutiérrez, H Mawi (2017)
On the numerical solution of the far field refractor problemNonlinear Anal., 157
Nestor Guillen, J. Kitagawa (2015)
Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian EquationsCommunications on Pure and Applied Mathematics, 70
J. Kitagawa (2012)
An iterative scheme for solving the optimal transportation problemCalculus of Variations and Partial Differential Equations, 51
The purpose of this paper is to present an iterative scheme to find approximate solutions, to any preset degree of accuracy, for a class of generated Jacobian equations introduced in Trudinger (Discrete Contin Dyn Syst 34(4): 1663–1681 2014). A proof of an upper bound on the number of iteration steps, without assuming any condition of Ma-Trudinger-Wang type, is presented. Applications to optimal mass transport and to the parallel reflector problem in optics are also provided.
Calculus of Variations and Partial Differential Equations – Springer Journals
Published: Jul 7, 2017
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