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On the Neumann Problem for Monge-Ampére Type Equations

Published online by Cambridge University Press:  20 November 2018

Feida Jiang ,
Neil S. Trudinger  and
Ni Xiang
Feida Jiang
Affiliation:
Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, P.R.China e-mail: jiangfeida@math.tsinghua.edu.cn
Neil S. Trudinger
Affiliation:
Centre for Mathematics and Its Applications, The Australian National University, Canberra ACT 0200, Australia e-mail: neil.trudinger@anu.edu.au
Ni Xiang
Affiliation:
Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, P.R.China e-mail: nixiang@hubu.edu.cn
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Abstract

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In this paper, we study the global regularity for regular Monge-Ampère type equations associated with semilinear Neumann boundary conditions. By establishing a priori estimates for second order derivatives, the classical solvability of the Neumann boundary value problem is proved under natural conditions. The techniques build upon the delicate and intricate treatment of the standard Monge-Ampère case by Lions, Trudinger, and Urbas in 1986 and the recent barrier constructions and second derivative bounds by Jiang, Trudinger, and Yang for the Dirichlet problem. We also consider more general oblique boundary value problems in the strictly regular case.

Keywords

35J6635J96semilinear Neumann problemMonge-Ampère type equationsecond derivative estimates
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 6 , 01 December 2016 , pp. 1334 - 1361
Copyright
Copyright © Canadian Mathematical Society 2016

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