Optimal regularity for phase transition problems with convection
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 4, p. 715-740
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In this paper we consider a steady state phase transition problem with given convection v. We prove, among other things, that the weak solution is locally Lipschitz continuous provided that $𝐯=D\xi$ and ξ is a harmonic function. Moreover, for continuous casting problem, i.e. when v is constant vector, we show that Lipschitz free boundaries are ${C}^{1}$ regular surfaces.

DOI : https://doi.org/10.1016/j.anihpc.2014.03.003
Classification:  35R35,  35J60,  35R37,  80A22
Keywords: Free boundary, Stefan problem, Phase transition, Convection, Lipschitz regularity, Viscosity solution
@article{AIHPC_2015__32_4_715_0,
author = {Karakhanyan, Aram L.},
title = {Optimal regularity for phase transition problems with convection},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {32},
number = {4},
year = {2015},
pages = {715-740},
doi = {10.1016/j.anihpc.2014.03.003},
zbl = {1329.35361},
mrnumber = {3390081},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2015__32_4_715_0}
}
Karakhanyan, Aram L. Optimal regularity for phase transition problems with convection. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 4, pp. 715-740. doi : 10.1016/j.anihpc.2014.03.003. http://www.numdam.org/item/AIHPC_2015__32_4_715_0/

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