Abstract

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 ⁣:R2→[0,+∞[H\colon\mathbb{R}^2 \rightarrow [0,+\infty[. Under suitable assumptions on Ω\Omega and HH, we also characterize the minimizers.

Author information

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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

Keywords

  • Anisotropic perimeter
  • relative isoperimetric inequalities
  • Wulff shape

Mathematics Subject Classification

52A40

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Suggested citation

F. Della Pietra, N. Gavitone. “Relative Isoperimetric Inequality in the Plane: the Anisotropic Case.” Journal of Convex Analysis 20 (2013), No. 1, 157–180. https://doi.org/10.68381/jca20010

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.