Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (4): 794-802.

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The Neumann Boundary Value Problems of Two Dimensional Monge-Ampère Equations

Xiang Ni, Shi Juhua, Wang Yu'e   

  1. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathmatics, Hubei University, Wuhan 430062
  • Received:2013-09-15 Revised:2015-03-15 Online:2015-08-25 Published:2015-08-25

Abstract:

In this paper, we prove the second order derivatives estimates of Monge-Ampère type equations with Neumann boundary condition, using the method of auxiliary function which reduce the global estimates to the boundary. Then, we obtain the existence and regularity of the classical solutions for the equations.

Key words: Two dimensional Monge-Ampè, re type equations, Neumann boundary condition, Second order derivatives estimates

CLC Number: 

  • O175.25
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