An equivalent path functional formulation of branched transportation problems
Lorenzo Brasco Filippo Santambrogio
We consider two models for branched transport: the one introduced in Bernot et al. (Publ Mat 49:417-451, 2005), which makes use of a functional defined on measures over the space of Lipschitz paths, and the path functional model presented in Brancolini et al. (J Eur Math Soc 8:415-434, 2006), where one minimizes some suitable action functional defined over the space of measure-valued Lipschitz curves, getting sort of a Riemannian metric on the space of probabilities, favouring atomic measures, with a cost depending on the masses of each of their atoms. We prove that modifying the latter model according to Brasco (Ann Mat Pura Appl 189:95-125, 2010), then the two models turn out to be equivalent.
keywords: Branched transport; irrigation patterns; path functionals.
Global compactness results for nonlocal problems
Lorenzo Brasco Marco Squassina Yang Yang

We obtain a Struwe type global compactness result for a class of nonlinear nonlocal problems involving the fractional $p-$Laplacian operator and nonlinearities at critical growth.

keywords: Fractional $p$-Laplacian variational methods global compactness
Stability of variational eigenvalues for the fractional $p-$Laplacian
Lorenzo Brasco Enea Parini Marco Squassina
By virtue of $\Gamma-$convergence arguments, we investigate the stability of variational eigenvalues associated with a given topological index for the fractional $p-$Laplacian operator, in the singular limit as the nonlocal operator converges to the $p-$Laplacian. We also obtain the convergence of the corresponding normalized eigenfunctions in a suitable fractional norm.
keywords: $\Gamma-$convergence. nonlocal eigenvalue problems Fractional $p-$Laplacian critical points

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