172 citations · 357 across the 38 of their papers we have counts for
54 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…
The role of topology and capacity in some bounds for principal frequencies
Francesco Bozzola, Lorenzo Brasco
We prove a lower bound on the sharp Poincaré-Sobolev embedding constants for general open sets, in terms of their inradius. We consider the following two situations: planar sets wi…
On Morrey's inequality in Sobolev-Slobodecki\uı spaces
Lorenzo Brasco, Francesca Prinari, Firoj Sk
We study the sharp constant in the Morrey inequality for fractional Sobolev-Slobodecki\uı spaces on the whole . By generalizing a recent work by Hynd and Seuffert, we…
On the spectrum of sets made of cores and tubes
Francesca Bianchi, Lorenzo Brasco, Roberto Ognibene
We analyze the spectral properties of a particular class of unbounded open sets. These are made of a central bounded ``core'', with finitely many unbounded tubes attached to it. We…
Sobolev embeddings and distance functions
Lorenzo Brasco, Francesca Prinari, Anna Chiara Zagati
On a general open set of the euclidean space, we study the relation between the embedding of the homogeneous Sobolev space into and the summability prop…
An optimal lower bound in fractional spectral geometry for planar sets with topological constraints
Francesca Bianchi, Lorenzo Brasco
We prove a lower bound on the first eigenvalue of the fractional Dirichlet-Laplacian of order on planar open sets, in terms of their inradius and topology. The result is optima…