caa a22 4500 605516049 CHVBK 20210128100712.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s00205-015-0872-z doi (NATIONALLICENCE)springer-10.1007/s00205-015-0872-z Faber-Krahn Inequalities for the Robin-Laplacian: A Free Discontinuity Approach [Elektronische Daten] [Dorin Bucur, Alessandro Giacomini] Isoperimetric inequalities for the principal eigenvalues of the Robin-Laplacian are interpreted as free discontinuity problems (of unusual type). We prove a full range of Faber-Krahn inequalities in a nonlinear setting and for non smooth domains, including the open case of the torsional rigidity. The key point of the analysis relies on regularity issues for free discontinuity problems in spaces of functions of bounded variation. As a byproduct, we obtain the best constants for a class of Poincaré inequalities with trace terms in $${\mathbb{R}^N}$$ R N . Springer-Verlag Berlin Heidelberg, 2015 Bucur Dorin Laboratoire de Mathématiques, CNRS UMR 5127 Université de Savoie, Campus Scientifique, 73376, Le-Bourget-du-Lac, France aut Giacomini Alessandro DICATAM, Sezione di Matematica, Università degli Studi di Brescia, Via Valotti 9, 25133, Brescia, Italy aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 757-824 0003-9527 218:2<757 2015 218 205 https://doi.org/10.1007/s00205-015-0872-z 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/s00205-015-0872-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bucur Dorin Laboratoire de Mathématiques, CNRS UMR 5127 Université de Savoie, Campus Scientifique, 73376, Le-Bourget-du-Lac, France aut NATIONALLICENCE 700 1- Giacomini Alessandro DICATAM, Sezione di Matematica, Università degli Studi di Brescia, Via Valotti 9, 25133, Brescia, Italy aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 757-824 0003-9527 218:2<757 2015 218 205