Abstract
In this article, we solve the Dirichlet boundary value problemwhere is a cylindrical domain, D is the Cauchy-Riemann operator , is a Clifford algebra-valued function, , , is a k-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.
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