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.

Geometric aspects of p-capacitary potentials / Pinamonti, Andrea; Mazzieri, Lorenzo; Fogagnolo, Mattia. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 36:4(2019), pp. 1151-1179. [10.1016/j.anihpc.2018.11.005]

Geometric aspects of p-capacitary potentials

Andrea Pinamonti;Lorenzo Mazzieri;Mattia Fogagnolo
2019

Abstract

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.
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Pinamonti, Andrea; Mazzieri, Lorenzo; Fogagnolo, Mattia
Geometric aspects of p-capacitary potentials / Pinamonti, Andrea; Mazzieri, Lorenzo; Fogagnolo, Mattia. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 36:4(2019), pp. 1151-1179. [10.1016/j.anihpc.2018.11.005]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/219618
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