Generalizations of the Dirichlet problem for bianalytic functions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910232706285568 |
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| author | Blair, William L. |
| author_facet | Blair, William L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18573 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalizations of the Dirichlet problem for bianalytic functions Blair, William L. Analysis of PDEs Complex Variables 30G20, 30E25, 30G30, 35J46, 30J99 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. |
| title | Generalizations of the Dirichlet problem for bianalytic functions |
| topic | Analysis of PDEs Complex Variables 30G20, 30E25, 30G30, 35J46, 30J99 |
| url | https://arxiv.org/abs/2605.18573 |