On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2013
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| _version_ | 1866908473564856320 |
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| author | Costabel, Martin Dauge, Monique |
| author_facet | Costabel, Martin Dauge, Monique |
| contents | The equivalence between the inequalities of Babuška-Aziz and Friedrichs for sufficiently smooth bounded domains in the plane has been shown by Horgan and Payne 30 years ago. We prove that this equivalence, and the equality between the associated constants, is true without any regularity condition on the domain. For the Horgan-Payne inequality, which is an upper bound of the Friedrichs constant for plane star-shaped domains in terms of a geometric quantity known as the Horgan-Payne angle, we show that it is true for some classes of domains, but not for all bounded star-shaped domains. We prove a weaker inequality that is true in all cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1303_6141 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne Costabel, Martin Dauge, Monique Numerical Analysis Functional Analysis The equivalence between the inequalities of Babuška-Aziz and Friedrichs for sufficiently smooth bounded domains in the plane has been shown by Horgan and Payne 30 years ago. We prove that this equivalence, and the equality between the associated constants, is true without any regularity condition on the domain. For the Horgan-Payne inequality, which is an upper bound of the Friedrichs constant for plane star-shaped domains in terms of a geometric quantity known as the Horgan-Payne angle, we show that it is true for some classes of domains, but not for all bounded star-shaped domains. We prove a weaker inequality that is true in all cases. |
| title | On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne |
| topic | Numerical Analysis Functional Analysis |
| url | https://arxiv.org/abs/1303.6141 |