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.

Classification: 35J25, 35J70

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 p-Laplace operator}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, publisher = {Elsevier}, volume = {29}, number = {1}, year = {2012}, pages = {83-108}, doi = {10.1016/j.anihpc.2011.09.002}, zbl = {1241.35221}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2012__29_1_83_0} }

Lewis, John L.; Nyström, Kaj. Regularity of flat free boundaries in two-phase problems for the p-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/item/AIHPC_2012__29_1_83_0/

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