A Priori Estimates for Solutions of Fully Nonlinear Equations with Convex Level Set
نویسندگان
چکیده
We derive an a priori C2,α estimate for solutions of the fully non-linear elliptic equation F(D2u) = 0, provided the level set Σ = {M | F(M) = 0} satisfies: (a) Σ∩ {M | TrM = t} is strictly convex for all constants t; (b) the angle between the identity matrix I and the normal Fij to Σ is strictly positive on the non-convex part of Σ. Moreover, we do not need any convexity assumption on F in the course of the proof for the two dimensional case, as the classical result indicates. .
منابع مشابه
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