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

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

2011-10-25

arxiv.org/abs/1110.5663v1

Mathematics

Complex Variables

Scientific paper

By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichl\'et 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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