On the Neumann Problem for Monge-Ampére Type Equations

Jiang, Feida ; Trudinger, Neil S. ; Xiang, Ni

Canadian journal of mathematics, Tome 68 (2016) no. 6, pp. 1334-1361

Résumé

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.

Détail

DOI : 10.4153/CJM-2016-001-3

Mots-clés : 35J66, 35J96, semilinear Neumann problem, Monge-Ampère type equation, second derivative estimates

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