Computation of capacity
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- by Thomas Ransford and Jérémie Rostand;
- Math. Comp. 76 (2007), 1499-1520
- DOI: https://doi.org/10.1090/S0025-5718-07-01941-2
- Published electronically: January 24, 2007
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Abstract:
This article introduces a method for computing upper and lower bounds for the logarithmic capacity of a compact plane set. If the set has the Hölder continuity property, then these bounds converge to the value of the capacity. A number of examples are discussed in detail, including the Cantor middle-third set, for which we estimate $c(E)\approx 0.220949102189507$.References
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Bibliographic Information
- Thomas Ransford
- Affiliation: Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4
- MR Author ID: 204108
- Email: ransford@mat.ulaval.ca
- Jérémie Rostand
- Affiliation: Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4
- Email: jrostand@mat.ulaval.ca
- Received by editor(s): January 18, 2005
- Received by editor(s) in revised form: July 6, 2005
- Published electronically: January 24, 2007
- Additional Notes: The first author was supported by grants from NSERC and the Canada Research Chairs program
The second author was supported by a grant from NSERC - © Copyright 2007 American Mathematical Society
- Journal: Math. Comp. 76 (2007), 1499-1520
- MSC (2000): Primary 65E05; Secondary 31A15, 90C05
- DOI: https://doi.org/10.1090/S0025-5718-07-01941-2
- MathSciNet review: 2299786