Optimal Regularity for phase transition problems with convection

Aram Karakhanyan

doi:10.1016/j.anihpc.2014.03.003

Optimal Regularity for phase transition problems with convection

Aram Karakhanyan

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

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=Dξv=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 C1C1 regular surfaces.

Original language	English
Pages (from-to)	715-740
Number of pages	26
Journal	Annales de l'Institut Henri Poincaré C
Volume	32
Issue number	4
Early online date	4 Apr 2014
DOIs	https://doi.org/10.1016/j.anihpc.2014.03.003
Publication status	Published - Jul 2015

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title = "Optimal Regularity for phase transition problems with convection",

abstract = "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=Dξv=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 C1C1 regular surfaces.",

author = "Aram Karakhanyan",

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AB - 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=Dξv=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 C1C1 regular surfaces.

U2 - 10.1016/j.anihpc.2014.03.003

DO - 10.1016/j.anihpc.2014.03.003

M3 - Article

SN - 0294-1449

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SP - 715

EP - 740

JO - Annales de l'Institut Henri Poincaré C

JF - Annales de l'Institut Henri Poincaré C

IS - 4

ER -

Optimal Regularity for phase transition problems with convection

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