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.
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