Author

Enrico Valdinoci

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Preprint Oct 2026

Regularity theory for non-local almost minimal surfaces via Euler-Lagrange inequalities at small scales

We extend the notion of non-local almost minimal sets introduced in [Dipierro, Valdinoci, and Villa, J. Math. Pures Appl. (2026)] by admitting lower-order powers for the remainder term. We combine classical techniques and a new, weaker version of the Euler-Lagrange inequalities (at a microscopic scale) to obtain $\math...

S. Dipierro, O. Savin, Enrico Valdinoci et al. · 0 citations

Preprint Oct 2026

Boundedness of Solutions to Nonlocal Systems

Under mild mass or energy assumptions, we prove uniform $L^\infty$ bounds for all distributional solutions of a multi-dimensional system of nonlocal semilinear equations. The setting comprises Ginzburg-Landau systems and Allen-Cahn equations, and the results obtained are new even for scalar equations.

S. Dipierro, J. G. da Silva, Giorgio Poggesi et al. · 0 citations

Preprint Oct 2026

On the Weyl tube formula for nonlocal perimeters

We study the asymptotic behaviour of the nonlocal perimeter of tubular neighbourhoods. For a closed $C^{1,1}$ submanifold of Euclidean space, we show that a suitable rescaling of the nonlocal perimeter of its tube converges to an explicit constant times the Hausdorff measure of the submanifold. The constant is the frac...

S. Dipierro, Jack Thompson, Enrico Valdinoci · 0 citations