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Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations II. A Priori Estimates and the Dirichlet Problem

  • Ha Tien NgoanEmail author
  • Thai Thi Kim Chung
Article
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Abstract

In this paper, we consider the Dirichlet problem for nonsymmetric Monge-Ampère type equations in which a skew-symmetric matrix is introduced. We establish uniform with respect to a class of skew-symmetric matrix bounds for δ-elliptic \(C^{2, \alpha }(\overline {{\Omega }})\)-solutions to the Dirichlet problem. Then, we prove the classical solvability of the Dirichlet problem, provided those skew-symmetric matrices are sufficiently small in some sense.

Keywords

Monge-Ampère type equations δ-elliptic solutions Second derivative estimates The method of continuity 

Mathematics Subject Classification (2010)

35J66 

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  2. 2.University of Transport TechnologyHanoiVietnam

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