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.
Cite this article
Mattia Fogagnolo, Lorenzo Mazzieri, Andrea Pinamonti, Geometric aspects of p-capacitary potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 4, pp. 1151–1179DOI 10.1016/J.ANIHPC.2018.11.005