Free boundary Monge-Ampère equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 60

In this paper, we consider a class of Monge-Ampère equations in a free boundary domain of ℝ2 where the value of the unknown function is prescribed on the free boundary. From a variational point of view, these equations describe an optimal transport problem from an a priori undetermined source domain to a prescribed target domain. We prove the existence and uniqueness of a variational solution to these Monge-Ampère equations under a singularity condition on the density function on the source domain. Furthermore, we provide regularity results under some conditions on the prescribed domain.

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DOI : 10.1051/cocv/2022048
Classification : 49, 35
Keywords: Mass transportation, duality, Monge-Ampère 
@article{COCV_2022__28_1_A60_0,
     author = {Sedjro, Marc},
     title = {Free boundary {Monge-Amp\`ere} equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {28},
     doi = {10.1051/cocv/2022048},
     mrnumber = {4474350},
     zbl = {1498.49035},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv/2022048/}
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Sedjro, Marc. Free boundary Monge-Ampère equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 60. doi: 10.1051/cocv/2022048

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