An Operator-Theoretic Existence Proof of Solutions to Planar Dirichlét Problems |
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Authors: | Timothy H McNicholl |
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Institution: | 1. Department of Mathematics, Lamar University, Beaumont, TX, 77713, USA
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Abstract: | 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. |
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