Volume 53, Issue 1
The Monge-Ampère Equation for Strictly (n−1)-convex Functions with Neumann Condition

Bin Deng

J. Math. Study, 53 (2020), pp. 66-89.

Published online: 2020-03

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  • Abstract

A $C^2$ function on $\mathbb{R}^n$ is called strictly $(n-1)$-convex if the sum of any $n-1$ eigenvalues of its Hessian is positive. In this paper, we establish a global $C^2$ estimates to the Monge-Ampère equation for strictly $(n-1)$-convex functions with Neumann condition. By the method of continuity, we prove an existence theorem for strictly $(n-1)$-convex solutions of the Neumann problems.

  • Keywords

Neumann problem, (n−1)-convex, elliptic equation.

  • AMS Subject Headings

35J60, 35A09

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

bingomat@mail.ustc.edu.cn (Bin Deng)

  • BibTex
  • RIS
  • TXT
@Article{JMS-53-66, author = {Deng , Bin}, title = {The Monge-Ampère Equation for Strictly (n−1)-convex Functions with Neumann Condition}, journal = {Journal of Mathematical Study}, year = {2020}, volume = {53}, number = {1}, pages = {66--89}, abstract = {

A $C^2$ function on $\mathbb{R}^n$ is called strictly $(n-1)$-convex if the sum of any $n-1$ eigenvalues of its Hessian is positive. In this paper, we establish a global $C^2$ estimates to the Monge-Ampère equation for strictly $(n-1)$-convex functions with Neumann condition. By the method of continuity, we prove an existence theorem for strictly $(n-1)$-convex solutions of the Neumann problems.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v53n1.20.04}, url = {http://global-sci.org/intro/article_detail/jms/15208.html} }
TY - JOUR T1 - The Monge-Ampère Equation for Strictly (n−1)-convex Functions with Neumann Condition AU - Deng , Bin JO - Journal of Mathematical Study VL - 1 SP - 66 EP - 89 PY - 2020 DA - 2020/03 SN - 53 DO - http://doi.org/10.4208/jms.v53n1.20.04 UR - https://global-sci.org/intro/article_detail/jms/15208.html KW - Neumann problem, (n−1)-convex, elliptic equation. AB -

A $C^2$ function on $\mathbb{R}^n$ is called strictly $(n-1)$-convex if the sum of any $n-1$ eigenvalues of its Hessian is positive. In this paper, we establish a global $C^2$ estimates to the Monge-Ampère equation for strictly $(n-1)$-convex functions with Neumann condition. By the method of continuity, we prove an existence theorem for strictly $(n-1)$-convex solutions of the Neumann problems.

Bin Deng. (2020). The Monge-Ampère Equation for Strictly (n−1)-convex Functions with Neumann Condition. Journal of Mathematical Study. 53 (1). 66-89. doi:10.4208/jms.v53n1.20.04
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