@article {2016,
	title = {Confinement of dislocations inside a crystal with a prescribed external strain},
	year = {2016},
	note = {Preprint SISSA 20/2016/MATE},
	abstract = {We study screw dislocations in an isotropic crystal undergoing antiplane shear.
In the framework of linear elasticity, by fixing a suitable boundary condition for the strain
(prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach.},
	url = {http://urania.sissa.it/xmlui/handle/1963/35247},
	author = {Ilaria Lucardesi and Marco Morandotti and Riccardo Scala and Davide Zucco}
}
@article {2015,
	title = {Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets},
	year = {2015},
	institution = {SISSA},
	abstract = {We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum.

Our techniques involve symmetry results {\`a} la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure.},
	url = {http://urania.sissa.it/xmlui/handle/1963/35140},
	author = {Dario Mazzoleni and Davide Zucco}
}
