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Geometric aspects of \(p\)-capacitary potentials. (English) Zbl 1422.35091

Summary: 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.

MSC:

35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J40 Boundary value problems for higher-order elliptic equations
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