1 citations · 2 across the 8 of their papers we have counts for
10 papers
Essential spectrum for the Laplacian
Lorenzo Brasco, Luca Briani, Giovanni Franzina
We introduce a variational notion of essential spectrum for the Dirichlet Laplacian. We then extend the classical Persson Theorem to this nonlinear setting. This result provide…
Low eigenvalues of the Laplacian in general open sets
Lorenzo Brasco, Luca Briani, Francesca Prinari
We consider the minmax Ljusternik-Schnirelmann levels of the constrained Dirichlet integral, on a general open set of the Euclidean space. We show that, whenever one of these l…
Extremals for sharp Poincaré-Sobolev inequalities: periodically perforated sets and beyond
Lorenzo Brasco, Luca Briani, Francesca Prinari
We consider periodically perforated unbounded open sets and prove existence of extremals for the relevant sharp Poincaré-Sobolev embedding constant. The existence result holds no m…
Extremals for Poincaré-Sobolev sharp constants in Steiner symmetric sets
Lorenzo Brasco, Luca Briani, Francesca Prinari
We prove existence of minimizers for the sharp Poincaré-Sobolev constant in general Steiner symmetric sets, in the subcritical and superhomogeneous regime. The sets considered are…
Energy concentration in a two-dimensional magnetic skyrmion model: variational analysis of lattice and continuum theories
Luca Briani, Marco Cicalese, Leonard Kreutz
We investigate the formation of singularities in a baby Skyrme type energy model, which describes magnetic solitons in two-dimensional ferromagnetic systems. In presence of a diver…
Mean-to-max ratio of the torsion function and honeycomb structures
Luca Briani, Dorin Bucur
In this paper we study extremal behaviors of the mean to max ratio of the -torsion function with respect to the geometry of the domain. For larger than the dimension of the…
On a reverse Kohler-Jobin inequality
Luca Briani, Giuseppe Buttazzo, Serena Guarino Lo Bianco
We consider the shape optimization problems for the quantities , where varies among open sets of with a prescribed Lebesgue measure. While the charac…
On a class of Cheeger inequalities
Luca Briani, Giuseppe Buttazzo, Francesca Prinari
We study a general version of the Cheeger inequality by considering the shape functional . The infimum and the supremum of $\mathcal…
A shape optimization problem on planar sets with prescribed topology
L. Briani, G. Buttazzo, F. Prinari
We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form $P(…
Some inequalities involving perimeter and torsional rigidity
L. Briani, G. Buttazzo, F. Prinari
We consider shape functionals of the form on the class of open sets of prescribed Lebesgue measure. Here is fixed, denotes the perimeter of and…