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Acta Mathematica Vietnamica

, Volume 44, Issue 2, pp 469–491 | Cite as

Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations I: the d-Concavity and the Comparison Principle

  • Ha Tien NgoanEmail author
  • Thai Thi Kim Chung
Article

Abstract

We introduce the notion of d-concavity, d ≥ 0, and prove that the nonsymmetric Monge-Ampère type function of matrix variable is concave in an appropriate unbounded and convex set. We prove also the comparison principle for nonsymmetric Monge-Ampère type equations in the case when they are so-called δ-elliptic with respect to compared functions with 0 ≤ δ < 1.

Keywords

d-concavity δ-elliptic solution The comparison principle 

Mathematics Subject Classification (2010)

35J66 

Notes

References

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

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

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