5 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…