Author

Federico Pasqualotto

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Preprint Aug 2026

Morrey's problem in $\mathbb{R}^{2 \times 4}$ and $\mathbb{R}^{3 \times 3}_\mathrm{sym}$

We find an explicit rank-one convex non-quasiconvex integrand in $\mathbb{R}^{2\times 4}$: to falsify the quasiconvexity inequality, we exhibit a map $\mathbb{T}^4\to \mathbb{R}^2$ with $12$ non-zero Fourier modes. In fact, this map is obtained from a scalar potential, so we also find a rank one convex integrand in $\m...

Andrea Agazzi, Giuseppe Bruno, André Guerra et al. · 0 citations

Preprint Sep 2026

Quantitative Diffusive Limits for Singular Nonlocal Transport

We study the nonlocal continuity equation \[ \partial_t\mu_b =\operatorname{div}\!\left( \mu_b\nabla\log\bigl((I-b^2\Delta)^{-1}\mu_b\bigr) \right) \] on a closed connected Riemannian manifold. For smooth strictly positive initial data, we prove that as $b \to 0$, its global solution converges to heat flow $\mu(t)$ at...

Andrea Agazzi, Giuseppe Bruno, Federico Pasqualotto et al. · 0 citations