4 papers
On the stability of proximal operators in Wasserstein spaces under different notions of convexity
Simone Di Marino, Sara Farinelli, Emanuele Naldi
The proximal operator is a fundamental tool in variational analysis and optimization. In the setting of a Hilbert space, given a proper, lower semicontinuous convex functional, its…
Pleijel nodal domain theorem in non-smooth setting
Nicolò De Ponti, Sara Farinelli, Ivan Yuri Violo
We prove the Pleijel theorem in non-collapsed RCD spaces, providing an asymptotic upper bound on the number of nodal domains of Laplacian eigenfunctions. As a consequence, we obtai…
Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances
Nicolò De Ponti, Sara Farinelli
In the paper we prove two inequalities in the setting of spaces using similar techniques. The first one is an indeterminacy estimate involving the -Wassers…
Indeterminacy estimates and the size of nodal sets in singular spaces
Fabio Cavalletti, Sara Farinelli
We obtain the sharp version of the uncertainty principle recently introduced in [47], and improved by [13], relating the size of the zero set of a continuous function having zero m…