Neumann problem for overdetermined system related with almost complex structure
The author considers an overdetermined system of differential equations which is a generalization of both the Cauchy-Riemann equations and the Beltrami equation. In other words the author considers the Neumann problem for the operator \[ \mu \overline\partial=\overline\partial-\mu^ k \wedge \partial_ K \] \[ \text{where } \mu^ K= \mu^ K_ j d \overline z^ j,\;\partial_ K={\partial \over \partial z^ K};\;z^ K \in \mathbb{C}^ n. \] The author proves for example that the domain on which the problem can be solved can be transformed to a strongly pseudoconvex domain by a one-to-one \(\mu\)-holomorphic mapping.
scientific article; zbMATH DE number 98073