Beltrami equations associated with $ \beta $-analytic functions under different boundary conditions

Chaojun Wang; Yanyan Cui; Chaojun Wang; Yanyan Cui

doi:10.3934/math.20261177

AIMS Mathematics

2026, Volume 11, Issue 9: 29672-29695. doi: 10.3934/math.20261177

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Research article

Beltrami equations associated with $ \beta $-analytic functions under different boundary conditions

Chaojun Wang ,
Yanyan Cui ^,

College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466001, China

Received: 06 July 2026 Revised: 21 August 2026 Accepted: 01 September 2026 Published: 14 September 2026
MSC : 30C45, 32A30

In this paper, several fundamental boundary value problems of $ \beta $-analytic functions were discussed on the unit disc. First, the fundamental properties of $ \beta $-analytic functions were investigated. On this basis, the Dirichlet boundary value problems for $ \beta $-analytic functions were discussed, and the solutions and solvability conditions for these problems were derived. Then, the Neumann and half-Neumann boundary value problems associated with $ \beta $-analytic functions were further studied. Finally, the Rubin boundary value problems of $ \beta $-analytic functions were addressed and the explicit solutions and their solvability criteria were fully characterized.
- $ \beta $-analytic functions,
- Dirichlet problems,
- Neumann problems,
- Rubin problems
Citation: Chaojun Wang, Yanyan Cui. Beltrami equations associated with $ \beta $-analytic functions under different boundary conditions[J]. AIMS Mathematics, 2026, 11(9): 29672-29695. doi: 10.3934/math.20261177

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Abstract

In this paper, several fundamental boundary value problems of $ \beta $-analytic functions were discussed on the unit disc. First, the fundamental properties of $ \beta $-analytic functions were investigated. On this basis, the Dirichlet boundary value problems for $ \beta $-analytic functions were discussed, and the solutions and solvability conditions for these problems were derived. Then, the Neumann and half-Neumann boundary value problems associated with $ \beta $-analytic functions were further studied. Finally, the Rubin boundary value problems of $ \beta $-analytic functions were addressed and the explicit solutions and their solvability criteria were fully characterized.

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