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A priori estimates for solutions of fully nonlinear special Lagrangian equations. (English) Zbl 0988.35058
Summary: We derive an a priori C 2,α estimate in dimension three for the equation F(D 2 u)=arctanλ 1 +arctanλ 2 +arctanλ 3 =c, where λ 1 ,λ 2 ,λ 3 are the eigenvalues of the Hessian D 2 u. For -π/2<c<π/2, the c-level set of F(D 2 u) fails the convexity condition. Note that for any solution u of the above equation, (x,u(x)) is a minimizing graph in 6 . For c=0, ±π, the equation is equivalent to Δu=detD 2 u.
35J60Nonlinear elliptic equations
35B45A priori estimates for solutions of PDE