Notes on generalized special Lagrangian equation (2311.14260v1)

Published 24 Nov 2023 in math.AP

Abstract: We obtain a prior $C^{1,1}$ estimates for some Hessian (quotient) equations with positive Lipschitz right hand sides, through studying a twisted special Lagrangian equation. The results imply the interior $C^{2,\alpha}$ regularity for $C^0$ viscosity solutions to $\sigma_2=f^2(x)$ in dimension 3, with positive Lipschitz $f(x)$.

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Xingchen Zhou

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