Geodesic
On the Neumann Problem for Monge-Ampére Type Equations
Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1334-1361

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DOI

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.
DOI : 10.4153/CJM-2016-001-3
Mots-clés : 35J66, 35J96, semilinear Neumann problem, Monge-Ampère type equation, second derivative estimates 
Jiang, Feida; Trudinger, Neil S.; Xiang, Ni. On the Neumann Problem for Monge-Ampére Type Equations. Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1334-1361. doi: 10.4153/CJM-2016-001-3
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     title = {On the {Neumann} {Problem} for {Monge-Amp\'ere} {Type} {Equations}},
     journal = {Canadian journal of mathematics},
     pages = {1334--1361},
     year = {2016},
     volume = {68},
     number = {6},
     doi = {10.4153/CJM-2016-001-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-001-3/}
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