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Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius
Nicola Soave, Hugo Tavares, Alessandro Zilio
Consider the class of optimal partition problems with long range interactions \[ \inf \left\{ \sum_{i=1}^k λ_1(ω_i):\ (ω_1,\ldots, ω_k) \in \mathcal{P}_r(Ω) \right\}, \] where $λ_1…
Regularity of all minimizers of a class of spectral partition problems
Hugo Tavares, Alessandro Zilio
We study a rather broad class of optimal partition problems with respect to monotone and coercive functional costs that involve the Dirichlet eigenvalues of the partitions. We show…
Predator-prey models with competition, Part II: uniform regularity estimates
Henri Berestycki, Alessandro Zilio
We study a system of elliptic equations with strong competition and an arbitrary large number of components. The system is related to a model of predators and prey, with a single a…
Predator-prey models with competition, Part III: Classification of stationary solutions
Henri Berestycki, Alessandro Zilio
For a stationary system representing prey and groups of competing predators, we show classification results about the set of positive solutions. In particular, we show that if…
Regularity results for segregated configurations involving fractional Laplacian
Giorgio Tortone, Alessandro Zilio
We study the regularity of segregated profiles arising from competition - diffusion models, where the diffusion process is of nonlocal type and is driven by the fractional Laplacia…
Competition in periodic media: III -- Existence \& stability of segregated periodic coexistence states
Léo Girardin, Alessandro Zilio
In this paper we consider a system of parabolic reaction-diffusion equations with strong competition and two related scalar reaction-diffusion equations. We are mainly concerned wi…