On an Inequality of the Kolmogorov Type for a Second-Order Differential Expression

Beynon, Malcolm James ORCID: https://orcid.org/0000-0002-5757-270X, Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591 and Evans, William Desmond 1993. On an Inequality of the Kolmogorov Type for a Second-Order Differential Expression. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 442 (1916) , pp. 555-569. 10.1098/rspa.1993.0121

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Abstract

In this paper we discuss an integro-differential inequality formed from the square of a second-order differential expression. A connection between the existence of the inequality and the Titchmarsh-Weyl m-function is established and it is shown that the best constant in the inequality is determined by the behaviour of the m-function. Analytic results are established for specific classes of problems. A numerical treatment of the inequality is also discussed and estimates of the best constant in specific examples are given.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Business (Including Economics) Computer Science & Informatics Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Royal Society
ISSN:	1364-5021
Last Modified:	21 Oct 2022 09:51
URI:	https://orca.cardiff.ac.uk/id/eprint/38033

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