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math.AP2021
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…
math.AP2021★ 6 cited
Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds
Matteo Muratori, Nicola Soave
The Cartan-Hadamard conjecture states that, on every -dimensional Cartan-Hadamard manifold , the isoperimetric inequality holds with Euclidean optimal constant,…