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Second-derivative estimates for solutions of two-dimensional Monge-Ampère equations

Author: Friedmar Schulz
Journal: Proc. Amer. Math. Soc. 111 (1991), 101-110
MSC: Primary 35B45; Secondary 35J60
MathSciNet review: 1031671
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Abstract: Heinz-Lewy type a priori estimates are derived for the absolute values of the second derivatives of solutions $ z(x,y) \in {C^{1,1}}(\Omega )$ of Monge-Ampère equations of the general form

$\displaystyle Ar + 2Bs + Ct + (rt - {s^2}) = E$

in the interior of the domain $ \Omega $. The coefficients $ A,B,C,E$ depend in particular on the gradient of $ z(x,y)$ and satisfy certain structural conditions.

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Keywords: Fully nonlinear elliptic equations, Monge-Ampère equations, quasilinear elliptic systems, Heinz-Lewy systems, regularity, a priori estimates, characteristics, uniformization, conformal mappings, convex surfaces
Article copyright: © Copyright 1991 American Mathematical Society

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