Electron. J. Diff. Equ., Vol. 2015 (2015), No. 184, pp. 1-9.

L^p-continuity of solutions to parabolic free boundary problems

Abdeslem Lyaghfouri, El Mehdi Zaouche

In this article, we consider a class of parabolic free boundary problems. We establish some properties of the solutions, including L^infinity-regularity in time and a monotonicity property, from which we deduce strong L^p-continuity in time.

Submitted May 25, 2015. Published July 7, 2015.
Math Subject Classifications: 35B65, 35D30, 35R35.
Key Words: Parabolic equation; free boundary; monotonicity; L^p-continuity.

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Abdeslem Lyaghfouri
American University of Ras Al Khaimah
Department of Mathematics and Natural Sciences
Ras Al Khaimah, UAE
email: abdeslem.lyaghfouri@aurak.ac.ae
El Mehdi Zaouche
Ecole Normale Supérieure
Département de Mathématiques
16050 Kouba, Alger, Algérie
email: elmehdi-zaouche@univ-eloued.dz

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