25 citations · 190 across the 31 of their papers we have counts for
31 papers
Monotonicity Principle and "p-Laplace Signature" for Tomography in Nonlinear Elliptic Inverse Problems
Gianpaolo Piscitelli, Vincenzo Mottola, Antonello Tamburrino
This paper proposes a framework for treating the inverse obstacle problem for nonlinear elliptic equations with nonlinear materials. The problem is challenging because nonlinear ma…
First Eigenvalue and Torsional Rigidity: Isoperimetric Inequalities for the Fractional Laplacian
Barbara Brandolini, Ida de Bonis, Vincenzo Ferone +2
We present a fractional counterpart of a generalized Kohler-Jobin inequality, showing that, among all bounded, open sets with Lipschitz boundary, having the…
Monotonicity of the Laplace Transform for Tomography in Dissipative Systems
Antonello Tamburrino, Antonio Corbo Esposito, Gianpaolo Piscitelli
This paper addresses the problem of tomography for the interior of dissipative materials, with a focus on Magnetic Induction Tomography (MIT), a proven technique for imaging the in…
On the second anisotropic Cheeger constant and related questions
Gianpaolo Piscitelli
In this paper we study the behavior of the second eigenfunction of the anisotropic -Laplace operator \[ - Q_{p}u:=-\textrm{div} \left(F^{p-1}(\nabla u)F_ξ(\nabla u)\right), \] a…
The inverse obstacle problem for nonlinear inclusions
Vincenzo Mottola, Antonio Corbo Esposito, Luisa Faella +3
The Monotonocity Principle (MP), stating a monotonic relationship between a material property and a proper corresponding boundary operator, is attracting great interest in the fiel…
Symmetry results for a nonlocal nonlinear Poincaré-Wirtinger inequality
Gianpaolo Piscitelli
In this paper, we study the optimal constant in the nonlocal nonlinear Poincaré-Wirtinger inequality in : \begin{equation*} λ_α(p,q,r){\left(\int_{a}^{b}|u|^…
A sharp bound for the first Robin-Dirichlet eigenvalue
Nunzia Gavitone, Gianpaolo Piscitelli
In this paper, we study the first eigenvalue of the Laplacian on doubly connected domains when Robin and Dirichlet conditions are imposed on the outer and the inner part of the bou…
Tomography of nonlinear materials via the Monotonicity Principle
Vincenzo Mottola, Antonio Corbo Esposito, Gianpaolo Piscitelli +1
In this paper we present a first non-iterative imaging method for nonlinear materials, based on Monotonicity Principle. Specifically, we deal with the inverse obstacle problem, whe…
Symmetrization results for general nonlocal linear ellipitic and parabolic problems
Vincenzo Ferone, Gianpaolo Piscitelli, Bruno Volzone
We establish a Talenti-type symmetrization result in the form of mass concentration (i.e. integral comparison) for very general linear nonlocal elliptic problems, equipped with hom…
Imaging of nonlinear materials via the Monotonicity Principle
Vincenzo Mottola, Antonio Corbo Esposito, Gianpaolo Piscitelli +1
Inverse problems, which are related to Maxwell's equations, in the presence of nonlinear materials is a quite new topic in the literature. The lack of contributions in this area ca…
Piecewise nonlinear materials and Monotonicity Principle
Antonio Corbo Esposito, Luisa Faella, Vincenzo Mottola +3
This paper is focused on the Monotonicity Principle (MP) for nonlinear materials with piecewise growth exponent. This results are relevant because enables the use of a fast imaging…
The -Laplace "Signature" for Quasilinear Inverse Problems
A. Corbo Esposito, L. Faella, V. Mottola +3
This paper refers to an imaging problem in the presence of nonlinear materials. Specifically, the problem we address falls within the framework of Electrical Resistance Tomography…
The p-Laplace "Signature" for Quasilinear Inverse Problems with Large Boundary Data
A. Corbo Esposito, L. Faella, G. Piscitelli +2
This paper is inspired by an imaging problem encountered in the framework of Electrical Resistance Tomography involving two different materials, one or both of which are nonlinear.…
A stability result for the first Robin-Neumann eigenvalue: A double perturbation approach
Simone Cito, Gloria Paoli, Gianpaolo Piscitelli
Let , , where and are two open, bounded and convex sets such that and let be a given…
On the first Robin eigenvalue of the Finsler -Laplace operator as
Rosa Barbato, Francesco Della Pietra, Gianpaolo Piscitelli
Let be a bounded, connected, sufficiently smooth open set, and . In this paper, we study the -convergence, as , of the functional \[ J…
Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators
Francesco Della Pietra, Gianpaolo Piscitelli
The aim of this paper is to obtain optimal estimates for the first Robin eigenvalue of the anisotropic -Laplace operator, namely: \begin{equation*} λ_1(β,Ω)=\min_{ψ\in W^{1,p}(Ω…
A monotonicity result for the first Steklov-Dirichlet Laplacian eigenvalue
Nunzia Gavitone, Gianpaolo Piscitelli
In this paper, we consider the first Steklov-Dirichlet eigenvalue of the Laplace operator in annular domain with a spherical hole. We prove a monotonicity result with respect the h…
The Pseudo-orthogonality for Graph -Laplacian Eigenvectors and Applications to Higher Cheeger Constants and Data Clustering
Antonio Corbo Esposito, Gianpaolo Piscitelli
The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is a NP-hard problem that can be relaxed in the spectral graph theory,…
An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole
Nunzia Gavitone, Gloria Paoli, Gianpaolo Piscitelli +1
In this paper we prove the existence of a maximum for the first Steklov-Dirichlet eigenvalue in the class of convex sets with a fixed spherical hole under volume constraint. More p…
The Monotonicity Principle for Magnetic Induction Tomography
Antonello Tamburrino, Gianpaolo Piscitelli, Zhengfang Zhou
The inverse problem treated in this article consists in reconstructing the electrical conductivity from the free response of the system in the magneto-quasi-stationary (MQS) limit.…
A nonlocal anisotropic eigenvalue problem
Gianpaolo Piscitelli
We determine the shape which minimizes, among domains with given measure, the first eigenvalue of the anisotropic laplacian perturbed by an integral of the unknown function. Using…
Convex Symmetrization for Anisotropic Elliptic Equations with a lower order term
Gianpaolo Piscitelli
We use "generalized" version of total variation, coarea formulas, isoperimetric inequalities to obtain sharp estimates for solutions (and for their gradients) to anisotropic ellipt…
Monotonicity Principle in Tomography of Nonlinear Conducting Materials
Antonio Corbo Esposito, Luisa Faella, Gianpaolo Piscitelli +2
We treat an inverse electrical conductivity problem which deals with the reconstruction of nonlinear electrical conductivity starting from boundary measurements in steady currents…
An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes
Francesco Della Pietra, Gianpaolo Piscitelli
In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for the p-Laplacian operator in domains with convex holes. An analo…