The Neumann problem for Monge-Ampere type equations revisited.

Authors

DOI:

https://doi.org/10.53733/176

Keywords:

Neumann problem, Monge-Ampere type equation, second derivative estimates

Abstract

This 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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Author Biography

Feida Jiang, Southeast University, Nanjing,

School of Mathematics and Shing-Tung Yau Center of Southeast University, Professor

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Published

24-10-2021

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

Issue

Section

Vaughan Jones Memorial Special Issue