caa a22 4500 605515603 CHVBK 20210128100710.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00205-015-0845-2 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0845-2 On the Inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne [Elektronische Daten] [Martin Costabel, Monique Dauge] The equivalence between the inequalities of Babuška-Aziz and Friedrichs for sufficiently smooth bounded domains in the plane was shown by Horgan and Payne 30years 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. Springer-Verlag Berlin Heidelberg, 2015 Costabel Martin IRMAR UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France aut Dauge Monique IRMAR UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 873-898 0003-9527 217:3<873 2015 217 205 https://doi.org/10.1007/s00205-015-0845-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0845-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Costabel Martin IRMAR UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France aut NATIONALLICENCE 700 1- Dauge Monique IRMAR UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 873-898 0003-9527 217:3<873 2015 217 205