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arXiv · 2605.18573

Generalizations of the Dirichlet problem for bianalytic functions

William L. Blair
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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.

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William L. Blair. 2026-05-18. Generalizations of the Dirichlet problem for bianalytic functions. https://arxiv.org/abs/2605.18573

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