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Beyond Cheeger's constant
Lorenzo Brasco
The Cheeger constant of an open set of the Euclidean space is defined by minimizing the ratio "perimeter over volume", among all its smooth compactly contained subsets. We consider…
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…
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…
A Steklov version of the Torsional Rigidity
Lorenzo Brasco, María del Mar González, Mikel Ispizua
Motivated by the connection between the first eigenvalue of the Dirichlet-Laplacian and the torsional rigidity, the aim of this paper is to find a physically coherent and mathemati…
A sharp estimate a la calderon-zygmund for the p--laplacian
Lorenzo Brasco, Filippo Santambrogio
We consider local weak solutions of the Poisson equation for the p--Laplace operator. We prove a higher differentiability result, under an essentially sharp condition on the right-…