no. 5
Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 5, pp. 1259-1277.

We consider fully nonlinear obstacle-type problems of the form

{F(D2u,x)=f(x)a.e. in B1∩Ω,|D2u|≤Ka.e. in B1\Ω,
where Ω is an open set and K>0. In particular, structural conditions on F are presented which ensure that W2,n(B1) solutions achieve the optimal C1,1(B1/2) regularity when f is Hölder continuous. Moreover, if f is positive on B‾1, Lipschitz continuous, and {u≠0}⊂Ω, we obtain interior C1 regularity of the free boundary under a uniform thickness assumption on {u=0}. Lastly, we extend these results to the parabolic setting.

DOI : 10.1016/j.anihpc.2015.03.009
Classification : 35J60, 35K55, 35R35
Mots clés : Nonlinear elliptic equations, Nonlinear parabolic equations, Free boundaries, Regularity theory, Obstacle problems 
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Indrei, Emanuel; Minne, Andreas. Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 5, pp. 1259-1277. doi : 10.1016/j.anihpc.2015.03.009. http://archive.numdam.org/articles/10.1016/j.anihpc.2015.03.009/

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