The Neumann problem for Monge-Ampere type equations revisited.
Keywords:Neumann problem, Monge-Ampere type equation, second derivative estimates
AbstractThis paper concerns a priori second order derivative estimates of solutions of the Neumann problem for the Monge-Amp\`ere type equations in bounded domains in n dimensional Euclidean space. We first establish a double normal second order derivative estimate on the boundary under an appropriate notion of domain convexity. Then, assuming a barrier condition for the linearized operator, we provide a complete proof of the global second derivative estimate for elliptic solutions, as previously studied in our earlier work. We also consider extensions to the degenerate elliptic case, in both the regular and strictly regular matrix cases.
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How to Cite
Jiang, F., & Trudinger, N. (2021). The Neumann problem for Monge-Ampere type equations revisited. New Zealand Journal of Mathematics, 52, 671–689. https://doi.org/10.53733/176
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