Calculus of Variations and Geometric Measure Theory

M. Fogagnolo - L. Mazzieri - A. Pinamonti

Geometric aspects of p-capacitary potentials

created by pinamonti on 27 Mar 2018
modified by fogagnolo on 26 Oct 2020


Published Paper

Inserted: 27 mar 2018
Last Updated: 26 oct 2020

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2018


We provide monotonicity formulas for solutions to the p-Laplace equation defined in the exterior of a convex domain. A number of analytic and geometric consequences are derived, including the classical Minkowski inequality as well as new characterizations of rotationally symmetric solutions and domains. The proofs rely on the conformal splitting technique introduced by the second author in collaboration with V. Agostiniani.