Free boundary Monge-Ampère equations
| Autor: | Marc Sedjro |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | ESAIM: Control, Optimisation and Calculus of Variations. 28:60 |
| ISSN: | 1262-3377 1292-8119 |
| DOI: | 10.1051/cocv/2022048 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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