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Paper detail

An operator-theoretic existence proof of solutions to planar Dirichlét problems

By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichlét problems for planar Jordan domains with at least two boundary curves. An iterative method is thus obtained, and explicit bounds on the error in the resulting approximations are given. Finally, a closed form for the solution is given. No amount of differentiability of the boundary is assumed.

preprint2011arXivOpen access
Timothy H. McNicholl
math.CVmath.NA
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Timothy H. McNicholl

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