THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$∗

doi:10.1007/s10473-023-0408-9

Abstract

Abstract: k holomorphic functions are a type of generation of holomorphic functions. In this paper, a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in $\mathbb{C}^2$. The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel. Furthermore, the integral representation for the solution is obtained.

Key words: k holomorphic functions, boundary value problems, Cauchy type singular integral operators

Yanyan CUI, Zunfeng LI, Yonghong XIE, Yuying QIAO. THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$^∗[J].Acta mathematica scientia,Series B, 2023, 43(4): 1571-1586.

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THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$^∗

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