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NUMBER M21027
AUTHOR Lee, Taehun,Lee, Ki-Ahm
TITLE The obstacle problem for parabolic Monge-Ampere equation
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JOURNAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2022
ABSTRACT In this paper, we study the obstacle problem for the parabolic Monge-Ampere 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-Ampere equation with the forcing term f (x, t, u, Du). (C) 2021 Elsevier Inc. All rights reserved.
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