The Hodge Star Operator and the Beltrami Equation
Analysis of PDEs
2018-01-25 v1 Differential Geometry
Metric Geometry
Abstract
An essentially unique homeomorphic solution to the Beltrami equation was found in the 1960s using the theory of Calder\'{o}n-Zygmund and singular integral operators in . We will present an alternative method to solve the Beltrami equation using the Hodge star operator and standard elliptic PDE theory. We will also discuss a different method to prove the regularity of the solution. This approach is partially based on work by Dittmar.
Cite
@article{arxiv.1801.08109,
title = {The Hodge Star Operator and the Beltrami Equation},
author = {Eden Prywes},
journal= {arXiv preprint arXiv:1801.08109},
year = {2018}
}