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Class of hypocomplex structures on the two-dimensional torus. (English) Zbl 1421.35050
Summary: We study the Hölder solvability of a class of complex vector fields on the torus \(\mathbb{T}^2\). We make use of the Theta function to associate a Cauchy-Pompeiu type integral operator. A similarity principle for the solutions of the equation \(Lu=au+b\bar{u}\) is obtained.

MSC:
35F05 Linear first-order PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35C15 Integral representations of solutions to PDEs
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