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Luca Esposito

Publications and source records attributed to Luca Esposito.

12 recordsLinked to original sources
arXiv2026

Morrey estimates for the gradient in non-linear variational transmission problems

We study a class of variational transmission problems driven by nonlinear energies with discontinuous coefficients across a prescribed interface. The model setting consists of integral functionals of the form \[ \mathcal{F}(u;E)=\int_{\Omega}\sigma_E(x)\,F(\nabla u)\,dx, \] where the coefficient $\sigma_E$ takes two constant values on complementary regions separated by a $C^1$ hypersurface, and the integrand $F$ satisfies standard $p$-growth and monotonicity conditions with $p>2$. In this nonlinear variational framework, we establish local Morrey-space regularity for the gradient of local minimizers, proving that $\nabla u\in L^{2,\lambda}_{\mathrm{loc}}(\Omega)$ for every $0\leq\lambda<n$, provided $2<p<\frac{2n}{n-2}$. The proof is based on quantitative decay estimates for the energy near the interface, first obtained in a flat configuration and then extended to the general case by a suitable approximation argument.

math.AP↗
arXiv2025

Ahlfors-regularity for minimizers of a multiphase optimal design problem

We establish an Alhfors-regularity result for minimizers of a multiphase optimal design problem. It is a variant of the classical variational problem which involves a finite number of chambers $\mathcal{E}(i)$ of prescribed volume that partition a given domain $\Omega\subset\mathbb{R}^n$. The cost functional associated with a configuration $\left(\{\mathcal{E}(i)\}_i,u\right)$ is made up of the perimeter of the partition interfaces and a Dirichlet energy term, which is discontinuous across the interfaces. We prove that the union of the optimal interfaces is $(n-1)$-Alhfors-regular via a penalization method and decay estimates of the energy.

math.OC↗
arXiv2025

Finsler $p$-Laplacian in domains becoming unbounded

We study the asymptotic behavior of sequences of solutions, energies functionals, and the first eigenvalues associated with the Finsler $p$-Laplace operator, also known as the anisotropic $p$-Laplace operator on a sequence of bounded cylinders whose length tends to infinity. We prove that the solutions on the bounded cylinders converge to the solution on the cross-section, with a polynomial rate of convergence in the general case and exponential convergence in some special cases. We show that energies on finite cylinders, with the multiplication of a scaling factor, converge to the energy on the cross-section. Finally, we investigate the convergence of the first eigenvalue and, for a specific subclass, we provide the optimal convergence rate.

math.AP↗
arXiv2025

Quasiconvex Bulk and Surface Energies with subquadratic growth

We establish partial H\"older continuity of the gradient for equilibrium configurations of vectorial multidimensional variational problems, involving bulk and surface energies. The bulk energy densities are uniformly strictly quasiconvex functions with $p$-growth, $1<p< 2$, without any further structure conditions. The anisotropic surface energy is defined by means of an elliptic integrand $\Phi$ not necessarily regular.

math.OC↗
arXiv2022

Regularity Results for a free interface problem with Hölder coefficients

We study a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type albeit of very general form allowing the dependence from the unknown variable $u$ and the position $x$. We employ the regularity theory of $Λ$-minimizers to study the regularity of the free interface. The hallmark of the paper is the mild regularity assumption concerning the dependence of the coefficients with respect to $x$ and $u$ that is of Hölder type.

math.AP↗
arXiv2021

Regularity Results for an Optimal Design Problem with lower order terms

We study the regularity of the interface for optimal energy configurations of functionals involving bulk energies with an additional perimeter penalization of the interface. It is allowed the dependence on $(x,u)$ for the bulk energy. For a minimal configuration $(E,u)$, the Hölder continuity of $u$ is well known. We give an estimate for the singular set of the boundary $\partial E$. Namely we show that the Hausdorff dimension of the singular set is strictly smaller than $n-1$.

math.OC↗
arXiv2021

Design of adaptive optics by interference fitting: theoretical background

Interference-fit joints are typically adopted to produce permanent assemblies among mechanical parts. The resulting contact pressure is generally used for element fixing or to allow load transmission. Nevertheless, some special designs take advantage of the contact pressure to induce desiderata deformation or to mitigate the stress field inside the structure. Biased interference fitting between a planar mirror and an external ring could be used to induce the required curvature to realize new adaptive lens for optical aberration correction. Recently, thermally-actuated deformable mirror on this principle based, was proposed and prototyped. Although the feasibility and utility of such innovative lens was demonstrated, no comprehensive theory was developed to describe mirror behaviour and predict their curvature. Nowadays, the use of approximated numerical approach, such as the finite element method, is the only way to study the interaction between biased and interference fitted bodies. The paper aims to give the theoretical background for the correct design of adaptive lens actuated by interference fitting. A new formulation for the curvature prediction is proposed and compared with finite element analysis and available experimental measurements.

physics.optics↗
arXiv2020

On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded

We analyze the asymptotic behavior of the eigenvalues of nonlinear elliptic problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann) boundary conditions on domains becoming unbounded. We make intensive use of Picone identity to overcome nonlinearity complications. Altogether the use of Picone identity makes the proof easier with respect to the known proof in the linear case. Surprisingly the asymptotic behavior under mixed boundary conditions critically differs from the case of pure Dirichlet boundary conditions for some class of problems.

math.AP↗
arXiv2018

High-yield fabrication of entangled photon emitters for hybrid quantum networking using high-temperature droplet epitaxy

Several semiconductor quantum dot techniques have been investigated for the generation of entangled photon pairs. Among the other techniques, droplet epitaxy enables the control of the shape, size, density, and emission wavelength of the quantum emitters. However, the fraction of the entanglement-ready quantum dots that can be fabricated with this method is still limited to around 5%, and matching the energy of the entangled photons to atomic transitions (a promising route towards quantum networking) remains an outstanding challenge. Here, we overcome these obstacles by introducing a modified approach to droplet epitaxy on a high symmetry (111)A substrate, where the fundamental crystallization step is performed at a significantly higher temperature as compared to previous reports. Our method drastically improves the yield of entanglement-ready photon sources near the emission wavelength of interest, which can be as high as 95% due to the low values of fine structure splitting and radiative lifetime, together with the reduced exciton dephasing offered by the choice of GaAs/AlGaAs materials. The quantum dots are designed to emit in the operating spectral region of Rb-based slow-light media, providing a viable technology for quantum repeater stations.

cond-mat.mes-hall↗
arXiv2017

Ehrlich-Schwoebel Effect on the Growth Dynamics of GaAs(111)A surfaces

We present a detailed characterization of the growth dynamics of Ga(Al)As(111)A surfaces. We develop a theoretical growth model that well describes the observed behavior on the growth parameters and underlines the Ehrlich-Schwoebel barrier as leading factor that determines the growth dynamics. On such basis we analyze the factors that lead to the huge observed roughness on such surface orientations and we identify the growth conditions that drive the typical three-dimensional growth of Ga(Al)As(111)A towards atomically flat surface. GaAs/AlGaAs quantum wells realized on optimized surface (<0.2 nm roughness) show a record low emission linewidth of 4.5 meV.

cond-mat.mtrl-sci↗
arXiv2013

Topological aspects in the photonic crystal analog of single-particle transport in quantum Hall systems

We present a perturbative approach to derive the semiclassical equations of motion for the two-dimensional electron dynamics under the simultaneous presence of static electric and magnetic fields, where the quantized Hall conductance is known to be directly related to the topological properties of translationally invariant magnetic Bloch bands. In close analogy to this approach, we develop a perturbative theory of two-dimensional photonic transport in gyrotropic photonic crystals to mimic the physics of quantum Hall systems. We show that a suitable permittivity grading of a gyrotropic photonic crystal is able to simulate the simultaneous presence of analog electric and magnetic field forces for photons, and we rigorously derive the topology-related term in the equation for the electromagnetic energy velocity that is formally equivalent to the electronic case. A possible experimental configuration is proposed to observe a bulk photonic analog to the quantum Hall physics in graded gyromagnetic photonic crystals.

cond-mat.mes-hall↗