Geodesic
Optimal regularity for phase transition problems with convection
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 4, pp. 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=Dξ 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 : 10.1016/j.anihpc.2014.03.003
Classification : 35R35, 35J60, 35R37, 80A22
Keywords: Free boundary, Stefan problem, Phase transition, Convection, Lipschitz regularity, Viscosity solution 
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     title = {Optimal regularity for phase transition problems with convection},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {715--740},
     publisher = {Elsevier},
     volume = {32},
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     year = {2015},
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Karakhanyan, Aram L. Optimal regularity for phase transition problems with convection. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 4, pp. 715-740. doi: 10.1016/j.anihpc.2014.03.003

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