English

Dirichlet Problem of Quaternionic Monge-Amp\`ere Equations

Analysis of PDEs 2021-03-12 v3

Abstract

In this paper, the author studies quaternionic Monge-Amp\`ere equations and obtains the existence and uniqueness of the solutions to the Dirichlet problem for such equations without any restriction on domains. Our paper not only answers to the open problem proposed by Semyon Alesker in [3], but also extends relevant results in [7] to the quaternionic vector space.

Keywords

Cite

@article{arxiv.1403.3197,
  title  = {Dirichlet Problem of Quaternionic Monge-Amp\`ere Equations},
  author = {Jingyong Zhu},
  journal= {arXiv preprint arXiv:1403.3197},
  year   = {2021}
}

Comments

17 pages. All comments are welcome! To appear in Israel Journal of Mathematics. arXiv admin note: text overlap with arXiv:math/0606756 by other authors

R2 v1 2026-06-22T03:25:50.152Z