Brunn-Minkowski Inequality for the 1-Riesz Capacity and Level Set Convexity for the 1/2-Laplacian

Matteo Novaga; Berardo Ruffini

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

Fractional Laplacian
Brunn-Minkowski inequality
level set convexity
Riesz capacity

Suggested citation

M. Novaga, B. Ruffini. “Brunn-Minkowski Inequality for the 1-Riesz Capacity and Level Set Convexity for the 1/2-Laplacian.” Journal of Convex Analysis 22 (2015), No. 4, 1125–1134.