$$L^\infty $$-estimates in optimal transport for non quadratic costs
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Agueh, M.: Existence of solutions to degenerate parabolic equations via the Monge–Kantorovich theory. PhD thesis, Georgia Tech (2002)
Alberti, G., Ambrosio, L.: A geometrical approach to monotone functions in $$\mathbb{R}^n$$. Math. Z. 230, 259–316 (1999)
Ambrosio, L., Coscia, A., Dal Maso, G.: Fine properties of functions with bounded deformation. Arch. Ration. Mech. Anal. 139, 201–238 (1997)
Benamou, J.-D., Brenier, Y.: A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem. Numer. Mat. 84(3), 375–393 (2000)
Bouchitté, G., Jimenez, C., Mahadevan, R.: A new $$L^\infty $$ estimate in optimal mass transport. Proc. Am. Math. Soc. 135(11), 3525–3535 (2007)
Calderón, A.P., Zygmund, A.: Local properties of solutions of elliptic partial differential equations. Stud. Math. 20, 171–225 (1961)
Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton (1992)
Gutiérrez, C.E., Huang, Q.: The refractor problem in reshaping light beams. Arch. Ration. Mech. Anal. 193(2), 423–443 (2009)
Goldman, M., Otto, F.: A variational proof of partial regularity for optimal transportation maps. Ann. Sci. Ec. Norm. Sup. 53, 1209–1233 (2020) https://arxiv.org/pdf/1704.05339.pdf
Gutiérrez, C.E.: Optimal Transport and Applications to Geometric Optics. Lecture Notes (2021)
Gutiérrez, C.E., van Nguyen, T.: On Monge–Ampère type equations arising in optimal transportation problems. Calc. Var. Partial Differ. Equ. 28(3), 275–316 (2007)
Hörmander, L.: The Analysis of Linear Partial Differential Operators I. Grundlehren der mathematischen Wissenschaften, vol. 256, 2nd edn. Springer, Berlin (1990)
Mignot, F.: Contrôle dans les Inéquations Variationelles Elliptiques. J. Funct. Anal. 22, 130–185 (1976)
Otto, F., Prod’homme, M., Ried, T.: Variational approach to regularity of optimal transport maps: general cost functions. Ann. PDE 7, 17 (2021). https://doi.org/10.1007/s40818-021-00106-1
Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis, Grundlehren der mathematischen Wissenschaften, vol. 317, Springer (1998), Corrected 3rd. printing 2009. https://sites.math.washington.edu/~rtr/papers/rtr169-VarAnalysis-RockWets.pdf
Santambrogio, F.: Optimal Transport for Applied Mathematicians. Progress in Nonlinear Differential Equations and Their Applications, vol. 87. Birkhäuser, Boston (2015)
Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970)
Temam, R.: Problèmes Mathématiques en Plasticité. Gauthier-Villards, Paris (1983)