Riemann boundary value problem for H-2-monogenic function in Hermitian Clifford analysis
Department of Mathematics, Linyi University, Linyi, Shandong, 276005, P.R. China
Boundary Value Problems 2014, 2014:81 doi:10.1186/1687-2770-2014-81Published: 9 April 2014
Hermitian Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions of two Hermitian Dirac operators. Using a circulant matrix approach, we will study the Riemann type problems in Hermitian Clifford analysis. We prove a mean value formula for the Hermitian monogenic function. We obtain a Liouville-type theorem and a maximum module for the function above. Applying the Plemelj formula, integral representation formulas, and a Liouville-type theorem, we prove that the Riemann type problems for Hermitian monogenic and Hermitian-2-monogenic functions are solvable. Explicit representation formulas of the solutions are also given.