33 citations · 156 across the 35 of their papers we have counts for
12 papers · 1 filter
On the Serrin problem for ring-shaped domains: the -dimensional case
Virginia Agostiniani, Chiara Bernardini, Stefano Borghini +1
We provide several characterizations of ring-shaped rotationally symmetric solutions to the Serrin problem in arbitrary dimensions.
A note on the critical Laplace Equation and Ricci curvature
Mattia Fogagnolo, Andrea Malchiodi, Lorenzo Mazzieri
We study strictly positive solutions to the critical Laplace equation \[ - Δu = n(n-2) u^{\frac{n+2}{n-2}}, \] decaying at most like , on complete noncompact ma…
On the Serrin problem for ring-shaped domains
Virginia Agostiniani, Stefano Borghini, Lorenzo Mazzieri
In this paper, we deal with the long standing open problem of characterising rotationally symmetric solutions to , when Dirichlet boundary conditions are imposed on a ring…
A geometric capacitary inequality for sub-static manifolds with harmonic potentials
Virginia Agostiniani, Lorenzo Mazzieri, Francesca Oronzio
In this paper, we prove that associated with a sub-static asymptotically flat manifold endowed with a harmonic potential there is a one-parameter family of functions whic…
Minkowski Inequalities via Nonlinear Potential Theory
Virginia Agostiniani, Mattia Fogagnolo, Lorenzo Mazzieri
In this paper, we prove an extended version of the Minkowski Inequality, holding for any smooth bounded set , . Our proof relies on the discovery of…
Geometric aspects of p-capacitary potentials
Mattia Fogagnolo, Lorenzo Mazzieri, Andrea Pinamonti
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, in…