C 1 , α -estimates for the near field refractor
Gutiérrez, Cristian E.1 ; Tournier, Federico2
1 a Department of Mathematics, Temple University, Philadelphia, PA 19122, United States of America
2 b Instituto Argentino de Matemática A. P. Calderón, CONICET, Buenos Aires, Argentina
Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 577-600.
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We establish local C1,α estimates for one source near field refractors under structural assumptions on the target, and with no assumptions on the smoothness of the densities.

DOI : 10.1016/j.anihpc.2020.08.002
Mots-clés : Holder estimates, Geometric optics, Analysis of pdes, Regularity of weak solutions
Gutiérrez, Cristian E. 1 ; Tournier, Federico 2

1 a Department of Mathematics, Temple University, Philadelphia, PA 19122, United States of America
2 b Instituto Argentino de Matemática A. P. Calderón, CONICET, Buenos Aires, Argentina 
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     title = {$C^{1 , \alpha}$-estimates for the near field refractor},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {577--600},
     publisher = {Elsevier},
     volume = {38},
     number = {3},
     year = {2021},
     doi = {10.1016/j.anihpc.2020.08.002},
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Gutiérrez, Cristian E.; Tournier, Federico. $C^{1 , \alpha}$-estimates for the near field refractor. Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 577-600. doi : 10.1016/j.anihpc.2020.08.002. http://www.numdam.org/articles/10.1016/j.anihpc.2020.08.002/

[1] Abedin, F.; Gutiérrez, C.E. An iterative method for generated Jacobian equations, Calc. Var. Partial Differ. Equ., Volume 56 (2017) no. 101, pp. 1-14 | MR | Zbl

[2] Abedin, F.; Gutiérrez, C.E.; Tralli, G. C1,α-estimates for the parallel refractor, Nonlinear Anal., Volume 142 (2016), pp. 1-25 | DOI | MR | Zbl

[3] Caffarelli, L.A.; Gutiérrez, C.E.; Huang, Qingbo On the regularity of reflector antennas, Ann. Math., Volume 167 (2008), pp. 299-323 | DOI | MR | Zbl

[4] Guillén, Néstor A primer on generated Jacobian equations: geometry, optics, economics, Not. Am. Math. Soc., Volume 66 (2019) no. 9, pp. 1401-1411 | MR | Zbl

[5] Guillén, Néstor; Kitagawa, Jun Pointwise estimates and regularity in geometric optics and other generated Jacobian equations, Commun. Pure Appl. Math., Volume 70 (2017) no. 6, pp. 1146-1220 | DOI | MR | Zbl

[6] Gutiérrez, C.E.; Huang, Qingbo The near field refractor, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 31 (2014) no. 4, pp. 655-684 | DOI | Numdam | MR | Zbl

[7] C.E. Gutiérrez, H. Mawi, On the numerical solution of the near field refractor problem, Preprint, 2019. | MR

[8] Gutiérrez, C.E.; Tournier, F. Regularity for the near field parallel refractor and reflector problems, Calc. Var. Partial Differ. Equ., Volume 54 (2015) no. 1, pp. 917-949 | DOI | MR | Zbl

[9] Kim, Young-Heon; McCann, Robert J. Continuity, curvature, and the general covariance of optimal transportation, J. Eur. Math. Soc., Volume 12 (2010) no. 4, pp. 1009-1040 | DOI | MR | Zbl

[10] De Leo, R.; Gutiérrez, C.E.; Mawi, H. On the numerical solution of the far field refractor problem, Nonlinear Anal., Volume 157 (2017), pp. 123-145 | DOI | MR | Zbl

[11] Loeper, G. On the regularity of solutions of optimal transportation problems, Acta Math., Volume 202 (2009), pp. 241-283 | DOI | MR | Zbl

[12] Ma, Xi-Nan; Trudinger, N.; Wang, Xu-Jia Regularity of potential functions of the optimal transportation problem, Arch. Ration. Mech. Anal., Volume 177 (2005) no. 2, pp. 151-183 | DOI | MR | Zbl

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