| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 60 | |
| Number of page(s) | 23 | |
| DOI | https://doi.org/10.1051/cocv/2022048 | |
| Published online | 30 August 2022 | |
Free boundary Monge-Ampère equations
Humboldt-Universität zu Berlin Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany
* Corresponding author: sedjro.math@gmail.com
Received:
24
June
2021
Accepted:
4
July
2022
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.
Mathematics Subject Classification: 49 / 35
Key words: Mass transportation / duality / Monge-Ampère
© The authors. Published by EDP Sciences, SMAI 2022
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