Abstract:
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We prove the interior C2,α regularity of solutions for some nonconvex fully nonlinear elliptic
equations F(D2u, x) = f (x), x ∈ B1 ⊂ Rn. Our hypothesis is that, for every x ∈ B1, F(·,x) is the
minimum of a concave operator and a convex operator of D2u. This extends the Evans–Krylov theory
for convex equations to some nonconvex operators of Isaacs type. For instance, our results apply to
the 3-operator equation F3(D2u) = min{L1u,max{L2u,L3u}} = 0 (here Li are linear operators),
which motivated the present work.
2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. |