Geodesic
Regularity of flat free boundaries in two-phase problems for the p-Laplace operator
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 1, pp. 83-108
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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.

DOI : 10.1016/j.anihpc.2011.09.002
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 
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     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},
     year = {2012},
     publisher = {Elsevier},
     volume = {29},
     number = {1},
     doi = {10.1016/j.anihpc.2011.09.002},
     zbl = {1241.35221},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.09.002/}
}
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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, Tome 29 (2012) no. 1, pp. 83-108. doi: 10.1016/j.anihpc.2011.09.002

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