The Hodge Star Operator and the Beltrami Equation

الأصل · EN

An essentially unique homeomorphic solution to the Beltrami equation was found in the 1960s using the theory of Calderón-Zygmund and singular integral operators in Lᵖ(C). 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.