## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - A
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- Discrete & Continuous Dynamical Systems - S
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DCDS

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.

DCDS-S

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.

DCDS

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.

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