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 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 regular surfaces.
Mots-clés : 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}, pages = {715--740}, publisher = {Elsevier}, volume = {32}, number = {4}, year = {2015}, doi = {10.1016/j.anihpc.2014.03.003}, mrnumber = {3390081}, zbl = {1329.35361}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2014.03.003/} }
TY - JOUR AU - Karakhanyan, Aram L. TI - Optimal regularity for phase transition problems with convection JO - Annales de l'I.H.P. Analyse non linéaire PY - 2015 SP - 715 EP - 740 VL - 32 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2014.03.003/ DO - 10.1016/j.anihpc.2014.03.003 LA - en ID - AIHPC_2015__32_4_715_0 ER -
%0 Journal Article %A Karakhanyan, Aram L. %T Optimal regularity for phase transition problems with convection %J Annales de l'I.H.P. Analyse non linéaire %D 2015 %P 715-740 %V 32 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2014.03.003/ %R 10.1016/j.anihpc.2014.03.003 %G en %F 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, Tome 32 (2015) no. 4, pp. 715-740. doi : 10.1016/j.anihpc.2014.03.003. http://www.numdam.org/articles/10.1016/j.anihpc.2014.03.003/
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