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Elsa M. Marchini

Publications and source records attributed to Elsa M. Marchini.

7 recordsLinked to original sources
arXiv2026

On the Value Function for a Class of Set Motion Problems

The paper considers a class of optimal set motion problems, where the control determines the velocity of boundary points in the normal direction. Results and counterexamples are given, on the continuous dependence of the minimum cost from the initial configuration. The last sections of the paper study the slicing cost of bounded open sets. For strongly Lipschitz domains, it is proved that the slicing cost varies continuously w.r.t. the Hausdorff distance of the boundaries. We conjecture that the slicing cost for a disc is maximal among all sets with the same area.

math.OC↗
arXiv2026

Optimal Slicing Problems

Given a bounded open set $V\subset \mathbb{R}^2$, we consider the problem of slicing this set by a family of curves, whose average length is as small as possible. The first sections of the paper prove the existence of an optimal slicing and establish a connection with the problem of eradicating an invasive biological species from an island, considered in \cite{BMS}. Namely, an optimal slicing can be obtained as a limit of minimum time eradication strategies. The second part of the paper derives various necessary conditions for optimality, describing the behavior of an optimal slicing strategy in the interior of $V$ and near the boundary $\partial V$.

math.OC↗
arXiv2025

Optimally Controlled Moving Sets with Geographical Constraints

The paper is concerned with a family of geometric evolution problems, modeling the spatial control of an invasive population within a region $V\subset \R^2$ bounded by geographical barriers. If no control is applied, the contaminated set $Ω(t)\subset V$ expands with unit speed in all directions. By implementing a control, a region of area $M$ can be cleared up per unit time. Given an initial set $Ω(0)=Ω_0\subseteq V$, three main problems are studied: (1) Existence of an admissible strategy $t\mapstoΩ(t)$ which eradicates the contamination in finite time, so that $Ω(T)=\emptyset$ for some $T>0$. (2) Optimal strategies that achieve eradication in minimum time. (3) Strategies that minimize the average area of the contaminated set on a given time interval $[0,T]$. For these optimization problems, a sufficient condition for optimality is proved, together with several necessary conditions. Based on these conditions, optimal set-valued motions $t\mapsto Ω(t)$ are explicitly constructed in a number of cases. \end{abstract}

math.OC↗
arXiv2013

Global attractors for nonlinear viscoelastic equations with memory

We study the asymptotic properties of the semigroup S(t) arising from a nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain written in the past history framework of Dafermos. We establish the existence of the global attractor of optimal regularity for S(t) for a wide class of nonlinearities as well as within the most general condition on the memory kernel.

math.AP↗
arXiv2007

On Schoedinger operators with multipolar inverse-square potentials

Positivity, essential self-adjointness, and spectral properties of a class of Schroedinger operators with multipolar inverse-square potentials are discussed. In particular a necessary and sufficient condition on the masses of singularities for the existence of at least a configuration of poles ensuring the positivity of the associated quadratic form is established.

math.AP↗