Generalizations of the Dirichlet problem for bianalytic functions
Analysis of PDEs
2026-05-19 v1 Complex Variables
Abstract
We prove the Dirichlet problem for second-order iterated Vekua equations, a natural generalization of the Bitsadze equation, is well-posed when the boundary condition is defined as a product of an exponential function and a polynomial on a non-degenerate conic that is not a circumference. Also, we extend this result, as well as other related results for the Dirichlet problem for polyanalytic and generalized analytic functions from the literature, to their analogues for bicomplex differential equations.
Cite
@article{arxiv.2605.18573,
title = {Generalizations of the Dirichlet problem for bianalytic functions},
author = {William L. Blair},
journal= {arXiv preprint arXiv:2605.18573},
year = {2026}
}