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Zbl 0988.35058
Yuan, Yu
A priori estimates for solutions of fully nonlinear special Lagrangian equations. (English. French summary)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No.2, 261-270 (2001). ISSN 0294-1449

Summary: We derive an a priori $C^{2,\alpha}$ estimate in dimension three for the equation $F(D^2u)= \arctan\lambda_1 +\arctan\lambda_2 + \arctan \lambda_3=c$, where $\lambda_1,\lambda_2, \lambda_3$ are the eigenvalues of the Hessian $D^2u$. For $-\pi/2 <c<\pi/2$, the $c$-level set of $F(D^2u)$ fails the convexity condition. Note that for any solution $u$ of the above equation, $(x,\nabla u(x))$ is a minimizing graph in $\bbfR^6$. For $c=0$, $\pm\pi$, the equation is equivalent to $\Delta u=\det D^2u$.

MSC 2000:: *35J60 Nonlinear elliptic equations
35B45 A priori estimates

Keywords: eigenvalues of the Hessian; minimizing graph

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