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Regularisation of Abel's integral equation

Published online by Cambridge University Press:  14 November 2011

Dang Dinh Hai  and
Dang Dinh Ang
Dang Dinh Hai
Affiliation:
Department of Mathematics, Dai Hoc Tong Hop, HoChiMinh City University, Vietnam
Dang Dinh Ang
Affiliation:
Department of Mathematics, Dai Hoc Tong Hop, HoChiMinh City University, Vietnam
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Synopsis

Consider the Abel integral operator

where 0 < α < 1. Suppose u is in H1(0, 1) of H1-norm ≦E, and f is an element of L2(0, 1) such that ∥Au – f∥L−2 < ε. We give a regularised approximate solution uβ(f) of the equation

which satisfies

and can be computed simply by performing some integrations. The preceding error estimate can be sharpened by strengthening regularity conditions on u

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 1-2 , 1987 , pp. 165 - 168
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

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