Solving the Dirichlet problem constructively (2013)
Type of ContentJournal Article
PublisherUniversity of Canterbury. Mathematics and Statistics
The Dirichlet problem is of central importance in both applied and abstract potential theory. We prove the (perhaps surprising) result that the existence of solutions in the general case is an essentially nonconstructive proposition: there is no algorithm which will actually compute solutions for arbitrary domains and boundary conditions. A corollary of our results is the nonexistence of constructive solutions to the NavierStokes equations of fluid flow. But not all the news is bad: we provide reasonable conditions, omitted in the classical theory but easily satisfied, which ensure the computability of solutions.
CitationBridges, D.S., McKubre-Jordens, M. (2013) Solving the Dirichlet problem constructively. Journal of Logic and Analysis, 5(3), pp. 1-22.
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Keywordsconstructive analysis; Dirichlet problem; Brouwerian example; Markov’s principle; omniscience principle
ANZSRC Fields of Research01 - Mathematical Sciences::0103 - Numerical and Computational Mathematics::010399 - Numerical and Computational Mathematics not elsewhere classified
02 - Physical Sciences::0203 - Classical Physics::020303 - Fluid Physics
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McKubre-Jordens, M. (University of Canterbury. Mathematics and Statistics, 2013)
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