Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 20 (2013), No. 1, 157--180Copyright Heldermann Verlag 2013 The Relative Isoperimetric Inequality: the Anisotropic Case Francesco Della Pietra Università del Molise, Dipartimento S.A.V.A., Facoltà di Ingegneria, Via Duca degli Abruzzi, 86039 Termoli (CB), Italy francesco.dellapietra@unimol.it Nunzia Gavitone Università di Napoli, Dip. di Matematica e Applicazioni, 80126 Napoli, Italy nunzia.gavitone@unina.it [Abstract-pdf] We prove a relative isoperimetric inequality in the plane, when the perimeter is defined with respect to a convex, positively homogeneous function of degree one $H\colon\mathbb{R}^2 \rightarrow [0,+\infty[$. Under suitable assumptions on $\Omega$ and $H$, we also characterize the minimizers. Keywords: Anisotropic perimeter, relative isoperimetric inequalities, Wulff shape. MSC: 52A40 [ Fulltext-pdf  (254  KB)] for subscribers only.