Journal of Convex Analysis 22 (2015), No. 4, 1125--1134
Copyright Heldermann Verlag 2015
Brunn-Minkowski Inequality for the 1-Riesz Capacity and Level Set Convexity for the 1/2-Laplacian
Matteo Novaga
Dip. di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
novaga@dm.unipi.it
Berardo Ruffini
Institut Fourier, 100 Rue des Mathématiques, BP 74, 38402 St. Martin d'Hères, France
berardo.ruffini@ujf-grenoble.fr
We prove that that the 1-Riesz capacity satisfies a Brunn-Minkowski inequality, and that the capacitary function of the 1/2-Laplacian is level set convex.
Keywords: Fractional Laplacian, Brunn-Minkowski inequality, level set convexity, Riesz capacity.
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