In this paper we continue the study in Lewis and Nyström (2010) [19], concerning the regularity of the free boundary in a general two-phase free boundary problem for the p-Laplace operator, by proving regularity of the free boundary assuming that the free boundary is close to a Lipschitz graph.

Keywords:

*p*-Harmonic function,

*p*-Subharmonic, Free boundary, Two-phase, Boundary Harnack inequality, Hopf boundary principle, Lipschitz domain,

*ϵ*-Monotone, Monotone, Regularity

@article{AIHPC_2012__29_1_83_0, author = {Lewis, John L. and Nystr\"om, Kaj}, title = {Regularity of flat free boundaries in two-phase problems for the {\protect\emph{p}-Laplace} operator}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {83--108}, publisher = {Elsevier}, volume = {29}, number = {1}, year = {2012}, doi = {10.1016/j.anihpc.2011.09.002}, zbl = {1241.35221}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.09.002/} }

TY - JOUR AU - Lewis, John L. AU - Nyström, Kaj TI - Regularity of flat free boundaries in two-phase problems for the p-Laplace operator JO - Annales de l'I.H.P. Analyse non linéaire PY - 2012 SP - 83 EP - 108 VL - 29 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2011.09.002/ DO - 10.1016/j.anihpc.2011.09.002 LA - en ID - AIHPC_2012__29_1_83_0 ER -

%0 Journal Article %A Lewis, John L. %A Nyström, Kaj %T Regularity of flat free boundaries in two-phase problems for the p-Laplace operator %J Annales de l'I.H.P. Analyse non linéaire %D 2012 %P 83-108 %V 29 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2011.09.002/ %R 10.1016/j.anihpc.2011.09.002 %G en %F AIHPC_2012__29_1_83_0

Lewis, John L.; Nyström, Kaj. Regularity of flat free boundaries in two-phase problems for thep-Laplace operator. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 1, pp. 83-108. doi : 10.1016/j.anihpc.2011.09.002. http://www.numdam.org/articles/10.1016/j.anihpc.2011.09.002/

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