Abstract
Initial value problems of type can be solved by the contraction-mapping principle in case the initial function ϕ belongs to an associated space whose elements satisfy an interior estimate. The present article proves such an interior estimate in the sup-norm for generalized monogenic functions. The proof is based on a representation of generalized monogenic functions by harmonic functions. That way the article is another example for the technique of transforming solutions of simpler partial differential equations into solutions of more general ones (an overview on such methods can be found in Begehr's and Gilbert's two volumes [Begehr, H.G.W. and Gilbert, R.P., 1992/1993, Transformations, Transmutations and Kernel Functions, Vol. I and II (Harlow: Longman Scientific & Technical; New York: John Wiley & Sons, Inc.)].
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