A General Class of Free Boundary Problems for Fully Nonlinear Elliptic Equations

نویسندگان

  • ALESSIO FIGALLI
  • HENRIK SHAHGHOLIAN
  • Luis A. Caffarelli
چکیده

In this paper we study the fully nonlinear free boundary problem { F (Du) = 1 a.e. in B1 ∩ Ω |Du| ≤ K a.e. in B1 \ Ω, where K > 0, and Ω is an unknown open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that W 2,n solutions are locally C inside B1. Under the extra condition that Ω ⊃ {Du 6= 0} and a uniform thickness assumption on the coincidence set {Du = 0}, we also show local regularity for the free boundary ∂Ω ∩B1.

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تاریخ انتشار 2014