Dirichlet boundary value problem for monogenic functions in Clifford analysis.

In this article, we solve the Dirichlet boundary value problemwhereis a cylindrical domain,Dis the Cauchy-Riemann operator,is a Clifford algebra-valued function,,,is ak-dimensional submanifold of the boundary,,is a fixed point inside the domain. If the boundary data are Hölder continuously differentiable functions, then the unique solution is Hölder continuous. We shall prove an estimate of the solution by its boundary data. [ABSTRACT FROM AUTHOR]