On the Neumann problem for Monge-Amp\`ere type equations
Abstract
In this paper, we study the global regularity for regular Monge-Amp\`ere 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-Amp\`ere 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.
Cite
@article{arxiv.1502.02096,
title = {On the Neumann problem for Monge-Amp\`ere type equations},
author = {Feida Jiang and Neil S. Trudinger and Ni Xiang},
journal= {arXiv preprint arXiv:1502.02096},
year = {2015}
}
Comments
This version includes some additions and corrections. We are particularly grateful to a referee for careful reading and useful advice