arXiv subjects

Samuele Riccò

Publications and source records attributed to Samuele Riccò.

6 recordsLinked to original sources

arXiv2026

A regularity result for $BV^{\mathcal{A}}(Ω)$

It is well known that distributions whose symmetrized gradient is a bounded Radon measure belong to the space $BD$ on bounded domains with $\mathcal{C}^1$ boundary. In this work, we extend this result to a broader class of first-order linear elliptic operators. More precisely, let $\mathcal{A}$ be a first-order linear elliptic operator satisfying the rank-one property. We prove that if a distribution defined on a Lipschitz domain has bounded $\mathcal{A}$-variation, then it belongs to the space $BV^{\mathcal{A}}$.

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arXiv2026

Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems

In the first part of this paper we introduce the space of bounded deformation fields with generalized Orlicz growth. We establish their main properties, provide a modular representation, and characterize a decomposition of the modular into an absolutely continuous part and a singular part weighted via a recession function. A further analysis in the variable exponent case is also provided. The second part of the paper contains a notion of Musielak-Orlicz anisotropic Total Generalized Variation. We establish a duality representation, and show well-posedness of the corresponding image reconstruction problem.

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arXiv2025

Homogenization and linearization in magnetoelasticity under small elastic response

We perform a simultaneous homogenization and linearization analysis for a magnetoelastic energy functional featuring a mixed Eulerian-Lagrangian structure. Neglecting Zeeman and anisotropic contributions, we characterize the asymptotic behavior in the sense of Gamma-convergence for the sum of a nonlinear magnetoelastic energy, a symmetric exchange term defined on the actual configuration, and for the associated magnetostatic self-energy. After establishing compactness of displacements and magnetizations with equibounded energy, we identify the limiting energy functional as the sum of a quadratic homogenized magnetoelastic contribution with a limiting homogenized exchange and magnetostatic term. This is, to the authors' knowledge, the first homogenization result for manifold-valued mixed Eulerian-Lagrangian energies.

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arXiv2025

Global higher integrability and Hardy inequalities for double-phase functionals under a capacity density condition

We prove global higher integrability for functionals of double-phase type under a uniform local capacity density condition on the complement of the considered domain $Ω\subset \mathbb{R}^n$. In this context, we investigate a new natural notion of variational capacity associated to the double-phase integrand. Under the related fatness condition for the complement of $Ω$, we establish an integral Hardy inequality. Further, we show that fatness of $\mathbb{R}^n \setminus Ω$ is equivalent to a boundary Poincaré inequality, a pointwise Hardy inequality and to the local uniform $p$-fatness of $\mathbb{R}^n \setminus Ω$. We provide a counterexample that shows that the expected Maz'ya type inequality - a key intermediate step toward global higher integrability - does not hold with the notion of capacity involving the double-phase functional itself.

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arXiv2023

A necessary condition for extremality of solutions to autonomous obstacle problems with general growth

Let us consider the autonomous obstacle problem \begin{equation*} \min_v \int_ΩF(Dv(x)) \, dx \end{equation*} on a specific class of admissible functions, where we suppose the Lagrangian satisfies proper hypotheses of convexity and superlinearity at infinity. Our aim is to characterize the solution, which exists and it is unique, thanks to a primal-dual formulation of the problem. The proof is based on classical arguments of Convex Analysis and on Calculus of Variations' techniques.

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arXiv2021

Regularity for Obstacle Problems without Structure Conditions

This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurance of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap are needed. The main tool used here is a ingenious Lemma which reveals to be crucial because it allows us to move from the variational obstacle problem to the relaxed-functional-related one. This is fundamental in order to find the solutions' regularity that we intended to study. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients.

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