16 citations · 24 across the 14 of their papers we have counts for
18 papers
The -relaxed area of the graph of the vortex map: optimal upper bound
Giovanni Bellettini, Alaa Elshorbagy, Riccardo Scala
We compute an upper bound for the value of the -relaxed area of the graph of the vortex map , , $x \neq 0…
Upper bounds for the relaxed area of -valued Sobolev maps and its countably subadditive interior envelope
Giovanni Bellettini, Riccardo Scala, Giuseppe Scianna
Given a bounded open connected Lipschitz set , we show that the relaxed Cartesian area functional of a map $u\in W^{1,1}(Ω;\mathb…
Relaxed area of graphs of piecewise Lipschitz maps in the strict -convergence
Giovanni Bellettini, Simone Carano, Riccardo Scala
We compute the relaxed Cartesian area in the strict -convergence on a class of piecewise Lipschitz maps from the plane to the plane, having jump made of several curves allowed…
The relaxed area of -valued singular maps in the strict -convergence
Giovanni Bellettini, Simone Carano, Riccardo Scala
Given a bounded open set , we study the relaxation of the nonparametric area functional in the strict topology in , and compute it for vo…
A new approach to topological singularities via a weak notion of Jacobian for functions of bounded variation
Lucia De Luca, Riccardo Scala, Nicolas Van Goethem
We introduce a weak notion of -minors of gradients of a suitable subclass of functions. In the case of maps in such a notion extends…
A non-parametric Plateau problem with partial free boundary
Giovanni Bellettini, Roberta Marziani, Riccardo Scala
We consider a Plateau problem in codimension in the non-parametric setting. A Dirichlet boundary datum is given only on part of the boundary of a bounded convex do…
An optimization problem in thermal insulation with Robin boundary conditions
Francesco Della Pietra, Carlo Nitsch, Riccardo Scala +1
We study thermal insulating of a bounded body . Under a prescribed heat source , we consider a model of heat transfer between and the environmen…
Existence, energy identity and higher time regularity of solutions to a dynamic visco-elastic cohesive interface model
Matteo Negri, Riccardo Scala
We study the dynamics of visco-elastic materials coupled by a common cohesive interface (or, equivalently, {two single domains separated by} a prescribed cohesive crack) in the ant…
Nonlinear three-dimensional derivation of line tension for dislocations: quadratic growth
Adriana Garroni, Roberta Marziani, Riccardo Scala
In this paper we derive a line tension model for dislocations in 3d starting from a geometrically nonlinear elastic energy with quadratic growth. In the asymptotic analysis, as the…
Uniform distribution of dislocations in Peierls-Nabarro models for semi-coherent interfaces
Silvio Fanzon, Marcello Ponsiglione, Riccardo Scala
In this paper we introduce Peierls-Nabarro type models for edge dislocations at semi-coherent interfaces between two heterogeneous crystals, and prove the optimality of uniformly d…
On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions
Giovanni Bellettini, Alaa Elshorbagy, Maurizio Paolini +1
In this paper we estimate from above the area of the graph of a singular map taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2-…
Upscaling of screw dislocations with increasing tangential strain
Ilaria Lucardesi, Marco Morandotti, Riccardo Scala +1
The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The -limit of a suitable rescaling of the renormalized energy is characte…
Existence and regularity of solutions for an evolution model of perfectly plastic plates
Paolo Gidoni, Giovanni Battista Maggiani, Riccardo Scala
We continue the study of a dynamic evolution model for perfectly plastic plates, recently derived from three-dimensional Prandtl-Reuss plasticity. We extend the previous existence…
Confinement of dislocations inside a crystal with a prescribed external strain
Ilaria Lucardesi, Marco Morandotti, Riccardo Scala +1
A system of screw dislocations in an isotropic crystal undergoing antiplane shear is studied in the framework of linear elasticity. Imposing a suitable boundary condition for t…
A rigorous sharp interface limit of a diffuse interface model related to tumor growth
E. Rocca, R. Scala
In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter , representing the interface thi…
On the viscous Cahn-Hilliard equation with singular potential and inertial term
Riccardo Scala, Giulio Schimperna
We consider a relaxation of the viscous Cahn-Hilliard equation induced by the second-order inertial term~. The equation also contains a semilinear term of "singular"…
A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints
Riccardo Scala, Giulio Schimperna
We consider a viscoelastic body occupying a smooth bounded domain of under the effects of volumic traction forces. Inertial effects are considered: hence, the equation descri…
On the strongly damped wave equation with constraint
Elena Bonetti, Elisabetta Rocca, Riccardo Scala +1
A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in th…