an:06416630
Zbl 1312.35040
Wang, Liping; Xu, Zuoliang; Qiao, Yuying
The mixed boundary value problem for the inhomogeneous Cimmino system
EN
Bound. Value Probl. 2015, Paper No. 13, 16 p. (2015).
00342511
2015
j
35F05
cimmino system; quaternionic analysis; \(\psi\)-hyperholomorphic functions; Cimmino singular integral operator; mixed boundary value problem
Summary: In this article, we first propose a kind of mixed boundary value problem for the inhomogeneous Cimmino system, which consists of first order linear partial differential equations in \(\mathbb{R}^{4}\). Then, by using the one-to-one correspondence between the theory of quaternion valued hyperholomorphic functions and that of Cimmino system's solutions, we transform the problem as stated above into a problem related to the \(\psi\)-hyperholomorphic functions in quaternionic analysis. Moreover, we show the boundedness, H??lder continuity, and generalized derivatives of a kind of singular integral operator \(^{\psi }T_{\mathbb{C}^{2}}[g]\) related to \(\psi\)-hyperholomorphic functions in quaternionic analysis. Lastly, the solution of the mixed boundary value problem for the inhomogeneous Cimmino system is explicitly described.