The mixed boundary value problem for the inhomogeneous Cimmino system

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 R 4 . Then, by using the one-to-one correspondence between the theory of quaternion valued hyperholomorphic functions...

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Bibliographic Details
Published in:Boundary value problems 2015-01, Vol.2015 (1), p.1-16, Article 13
Main Authors: Wang, Liping, Xu, Zuoliang, Qiao, Yuying
Format: Article
Language:English
Subjects:
Analysis
Approximations and Expansions
Boundary value problems
Continuity
Derivatives
Difference and Functional Equations
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Ordinary Differential Equations
Partial Differential Equations
Quaternions
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Transforms
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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 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 ψ -hyperholomorphic functions in quaternionic analysis. Moreover, we show the boundedness, Hölder continuity, and generalized derivatives of a kind of singular integral operator T C 2 ψ [ g ] related to ψ -hyperholomorphic functions in quaternionic analysis. Lastly, the solution of the mixed boundary value problem for the inhomogeneous Cimmino system is explicitly described.
ISSN:1687-2770
1687-2770
DOI:10.1186/s13661-014-0273-5