The obstacle problem for parabolic Monge-Ampère equation
In this paper, we study the obstacle problem for the parabolic Monge-Ampère equation with the forcing term f(x,t,u,Du). We establish existence, uniqueness, and optimal regularity under some structure conditions via the penalization method and a priori estimates. Moreover, we discuss the regularity o...
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| Published in: | Journal of Differential Equations 2022-02, Vol.309, p.608-649 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | eng |
| Online Access: | Get full text |
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| Summary: | In this paper, we study the obstacle problem for the parabolic Monge-Ampère equation with the forcing term f(x,t,u,Du). We establish existence, uniqueness, and optimal regularity under some structure conditions via the penalization method and a priori estimates. Moreover, we discuss the regularity of the free boundary.
As a consequence of our approach, we also obtain the existence and uniqueness of the solution of the Cauchy-Dirichlet problem for the parabolic Monge-Ampère equation with the forcing term f(x,t,u,Du). |
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| ISSN: | 0022-0396 1090-2732 |