21 citations · 39 across the 17 of their papers we have counts for
25 papers
-Laplace Serrin problem on planar annuli
Virginia Agostiniani, Chiara Bernardini
We prove a rigidity result for the problem defined on a ring-shaped domain in , when homogeneous Dirichlet boundary conditions are imposed and .…
Estimates for the p-Green function near the pole
Stefano Borghini, Virginia Agostiniani
We study the asymptotic expansion of p-Green functions and their derivatives near the pole. In the Euclidean setting, we strengthen a theorem from [arXiv:2203.01206] by establishin…
Riemannian Penrose Inequality for Manifolds with Corners via Non-Linear Potential Theory
Virginia Agostiniani, Christina Karapiperi, Lorenzo Mazzieri
We present a new proof of the Positive Mass Theorem and the Riemannian Penrose Inequality for three-dimensional asymptotically flat Riemannian manifolds whose metrics fail to be $C…
Mass-type invariants in the presence of a cosmological constant
Virginia Agostiniani, Stefano Borghini, Lorenzo Mazzieri
In this paper, we introduce a new family of mass-type invariants for time-symmetric initial data in space-times satisfying the Dominant Energy Condition. For positive cosmological…
Singularly Perturbed Gradient Flows and Evolution of Critical Points in Infinite Dimensions
Virginia Agostiniani, Riccarda Rossi, Giuseppe Savaré
We consider singularly perturbed gradient flows in Hilbert spaces, driven by a time-dependent, nonconvex, and nonsmooth energy, and address the convergence of their solutions to cu…
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.
Riemannian Penrose inequality via Nonlinear Potential Theory
Virginia Agostiniani, Carlo Mantegazza, Lorenzo Mazzieri +1
We provide a new proof of the Riemannian Penrose inequality for time-symmetric asymptotically flat initial data with a single black-hole horizon. The proof proceeds through a newly…
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 Green's function proof of the Positive Mass Theorem
V. Agostiniani, L. Mazzieri, F. Oronzio
In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green's function of an a…
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…
Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
Virginia Agostiniani, Mattia Fogagnolo, Lorenzo Mazzieri
In this paper we consider complete noncompact Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth, of dimension . We prove a sharp…
Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets
Virginia Agostiniani, Alessandro Lucantonio, Danka Lučić
We rigorously derive a Kirchhoff plate theory, via -convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin…
Dimension reduction via Gamma-convergence for soft active materials
Virginia Agostiniani, Antonio DeSimone
We present a rigorous derivation of dimensionally reduced theories for thin sheets of nematic elastomers, in the finite bending regime. Focusing on the case of twist nematic textur…
Singular vanishing-viscosity limits of gradient flows: the finite-dimensional case
Virginia Agostiniani, Riccarda Rossi
In this note we study the singular vanishing-viscosity limit of a gradient flow set in a finite-dimensional Hilbert space and driven by a smooth, but possibly non convex, time-depe…
Monotonicity formulas in potential theory
Virginia Agostiniani, Lorenzo Mazzieri
Using the electrostatic potential due to a uniformly charged body , , we introduce a family of monotone quantities associated with the level set f…
Shape programming for narrow ribbons of nematic elastomers
Virginia Agostiniani, Antonio DeSimone, Konstantinos Koumatos
Using the theory of -convergence, we derive from three-dimensional elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e. ribbons exhibiting spontaneous c…
Rigorous derivation of active plate models for thin sheets of nematic elastomers
Virginia Agostiniani, Antonio DeSimone
In the context of finite elasticity, we propose plate models describing the spontaneous bending of nematic elastomer thin films due to variations along the thickness of the nematic…
On the geometry of the level sets of bounded static potentials
Virginia Agostiniani, Lorenzo Mazzieri
In this paper we present a new approach to the study of asymptotically flat static metrics arising in general relativity. In the case where the static potential is bounded, we intr…
Riemannian aspects of potential theory
Virginia Agostiniani, Lorenzo Mazzieri
In this paper we provide a new method for establishing the rotational symmetry of the solutions to a couple of very classical overdetermined problems arising in potential theory, i…
On the transversality conditions and their genericity
Virginia Agostiniani, Riccarda Rossi, Giuseppe Savaré
In this note we review some results on the transversality conditions for a smooth Fredholm map between two Banach spaces . These conditions are well-…
Attainment results for nematic elastomers
V. Agostiniani, G. Dal Maso, A. DeSimone
We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically lin…
From nonlinear to linearized elasticity via Gamma-convergence: the case of multiwell energies satisfying weak coercivity conditions
Virginia Agostiniani, Timothy Blass, Konstantinos Koumatos
Linearized elasticity models are derived, via Gamma-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and sa…
Stability in an overdetermined problem for the Green's function
Virginia Agostiniani, Rolando Magnanini
In the plane, we consider the problem of reconstructing a domain from the normal derivative of its Green's function (with fixed pole) relative to the Dirichlet problem for the Lapl…