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University of Canterbury

1. McKubre-Jordens, M. Solving the Dirichlet problem constructively.

Degree: Mathematics and Statistics, 2013, University of Canterbury

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.

Subjects/Keywords: constructive analysis; Dirichlet problem; Brouwerian example; Markov’s principle; omniscience principle; Field of Research::01 - Mathematical Sciences::0103 - Numerical and Computational Mathematics::010399 - Numerical and Computational Mathematics not elsewhere classified; Field of Research::02 - Physical Sciences::0203 - Classical Physics::020303 - Fluid Physics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

McKubre-Jordens, M. (2013). Solving the Dirichlet problem constructively. (Thesis). University of Canterbury. Retrieved from http://hdl.handle.net/10092/9136

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

McKubre-Jordens, M. “Solving the Dirichlet problem constructively.” 2013. Thesis, University of Canterbury. Accessed May 09, 2021. http://hdl.handle.net/10092/9136.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

McKubre-Jordens, M. “Solving the Dirichlet problem constructively.” 2013. Web. 09 May 2021.

Vancouver:

McKubre-Jordens M. Solving the Dirichlet problem constructively. [Internet] [Thesis]. University of Canterbury; 2013. [cited 2021 May 09]. Available from: http://hdl.handle.net/10092/9136.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

McKubre-Jordens M. Solving the Dirichlet problem constructively. [Thesis]. University of Canterbury; 2013. Available from: http://hdl.handle.net/10092/9136

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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