36 citations · 140 across the 28 of their papers we have counts for
29 papers
On the structure of entropy dissipation and regularity for quasi-entropy solutions to 1d scalar conservation laws and to isentropic Euler system with
Fabio Ancona, Elio Marconi, Luca Talamini
In this paper, we first investigate quasi-entropy solutions to scalar conservation laws in several space dimensions. In this setting, we introduce a suitable Lagrangian representat…
Rectifiability of entropy productions for weak solutions of the 2D eikonal equation with supercritical regularity
Xavier Lamy, Elio Marconi
Weak solutions of the eikonal equation \begin{align*} |m|=1\text{ a.e. and }\mathrm{div}\: m =0\,, \end{align*} arise naturally as shar…
On the regularity of continuous solutions to multidimensional scalar conservation laws with bounded source
Fabio Ancona, Laura Caravenna, Alexander J. Cliffe +1
We prove the Hölder regularity of continuous isentropic solutions to multi-dimensional scalar balance laws when the source term is bounded and the flux satisfies general assumption…
Well-posedness results for the Generalized Aw-Rascle-Zhang model
Elio Marconi, Laura V. Spinolo
We establish existence, uniqueness and stability results for the so-called Generalized Aw-Rascle-Zhang model, a second order traffic model introduced by Fan, Herty and Seibold. Our…
Nonlocal Generalized Aw-Rascle-Zhang model: well-posedness and singular limit
Elio Marconi, Laura V. Spinolo
We discuss a nonlocal version of the Generalized Aw-Rascle-Zhang model, a second-order vehicular traffic model where the empty road velocity is a Lagrangian marker governed by a tr…
Uniqueness Domains for Solutions of Hyperbolic Conservation Laws
Alberto Bressan, Elio Marconi, Ganesh Vaidya
For a genuinely nonlinear hyperbolic system of conservation laws, assuming that the initial data have small norm but possibly unbounded total variation…
Liouville type theorem and kinetic formulation for 2x2 systems of conservation laws
Fabio Ancona, Elio Marconi, Luca Talamini
We study entropy solutions to systems of conservation laws. We show that, if a uniformly convex entropy exists, these solutions satisfy a pair of kin…
Intermediate Domains for Scalar Conservation Laws
Fabio Ancona, Alberto Bressan, Elio Marconi +1
For a scalar conservation law with strictly convex flux, by Oleinik's estimates the total variation of a solution with initial data decay…
An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate
Maria Colombo, Gianluca Crippa, Elio Marconi +1
Consider a non-local (i.e., involving a convolution term) conservation law: when the convolution term converges to a Dirac delta, in the limit we formally recover a classical (or "…
Hölder regularity of continuous solutions to balance laws and applications in the Heisenberg group
Laura Caravenna, Elio Marconi, Andrea Pinamonti
We prove Hölder regularity of any continuous solution to a -D scalar balance law , when the source term is bounded and the flux is nonlinear of o…
Ole\uınik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit
Giuseppe Maria Coclite, Maria Colombo, Gianluca Crippa +5
We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term $W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast…
On Lebesgue points of entropy solutions to the eikonal equation
Xavier Lamy, Elio Marconi
We consider entropy solutions to the eikonal equation in two space dimensions. These solutions are motivated by a class of variational problems and fail in general t…
Enhanced dissipation for two-dimensional Hamiltonian flows
Elia Bruè, Michele Coti Zelati, Elio Marconi
Let be an autonomous, non-constant Hamiltonian on a compact -dimensional manifold, generating an incompressible velocity field . We give…
Stability of quasi-entropy solutions of non-local scalar conservation laws
Elio Marconi, Emanuela Radici, Federico Stra
We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequal…
Stability of the vortex in micromagnetics and related models
Xavier Lamy, Elio Marconi
We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply-connected bounded domain. Configurations of vanishing energy have been characterized by Jabin, Ot…
Nonlocal traffic models with general kernels: singular limit, entropy admissibility, and convergence rate
Maria Colombo, Gianluca Crippa, Elio Marconi +1
Nonlocal conservation laws (the signature feature being that the flux function depends on the solution through the convolution with a given kernel) are extensively used in the mode…
Generalized Characteristics for Finite Entropy Solutions of Burgers' Equation
Andres A. Contreras Hip, Xavier Lamy, Elio Marconi
We prove the existence of generalized characteristics for weak, not necessarily entropic, solutions of Burgers' equation \[ \partial_t u +\partial_x \frac{u^2}{2} =0, \] whose entr…
New regularity results for scalar conservation laws, and applications to a source-destination model for traffic flows on networks
Simone Dovetta, Elio Marconi, Laura V. Spinolo
We focus on entropy admissible solutions of scalar conservation laws in one space dimension and establish new regularity results with respect to time. First, we assume that the flu…
Initial-boundary value problems for merely bounded nearly incompressible vector fields in one space dimension
Simone Dovetta, Elio Marconi, Laura V. Spinolo
We establish existence and uniqueness results for initial-boundary value problems for transport equations in one space dimension with nearly incompressible velocity fields, under t…
Characterization of minimizers of Aviles-Giga functionals in special domains
Elio Marconi
We consider the singularly perturbed problem on bounded domains . Un…
Differentiability properties of the flow of 2d autonomous vector fields
Elio Marconi
We investigate under which assumptions the flow associated to autonomous planar vector fields inherits the Sobolev or BV regularity of the vector field. We consider nearly incompre…
Rectifiability of entropy defect measures in a micromagnetics model
Elio Marconi
We study the fine properties of a class of weak solutions of the eikonal equation arising as asymptotic domain of a family of energy functionals introduced in (Rivière T, Serfa…
The rectifiability of the entropy defect measure for Burgers equation
Elio Marconi
We consider bounded weak solutions to the Burgers equation for which every entropy dissipation is representable by a measure and we prove that all these measures are concentrated o…
Regularity estimates for the flow of BV autonomous divergence free vector fields in
Paolo Bonicatto, Elio Marconi
We consider the regular Lagrangian flow X associated to a bounded divergence-free vector field b with bounded variation. We prove a Lusin-Lipschitz regularity result for X and we s…