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On the Neumann Problem for Monge-Ampère Type Equations

  Published:2016-06-21
 Printed: Dec 2016
  • Feida Jiang,
    Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, P.R. China
  • Neil S Trudinger,
    Centre for Mathematics and Its Applications, The Australian National University, Canberra ACT 0200, Australia
  • Ni Xiang,
    Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, P.R. China
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Abstract

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: semilinear Neumann problem, Monge-Ampère type equation, second derivative estimates semilinear Neumann problem, Monge-Ampère type equation, second derivative estimates
MSC Classifications: 35J66, 35J96 show english descriptions Nonlinear boundary value problems for nonlinear elliptic equations
Elliptic Monge-Ampere equations
35J66 - Nonlinear boundary value problems for nonlinear elliptic equations
35J96 - Elliptic Monge-Ampere equations
 

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