J. Serra

activity

20112023

most citedBoundary regularity for fully nonlinear integro-differential equations

77 citations · 190 across the 25 of their papers we have counts for

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Showing 2021Show all

4 papers · 1 filter

math.AP2021★ 4 cited

Free boundary partial regularity in the thin obstacle problem

Federico Franceschini, Joaquim Serra

For the thin obstacle problem in $R^{n}$ , $n \geq 2$ , we prove that at all free boundary points, with the exception of a $(n - 3)$ -dimensional set, the solution differs from it…

math.AP2021★ 3 cited

Stable solutions to the fractional Allen-Cahn equation in the nonlocal perimeter regime

Xavier Cabre, Eleonora Cinti, Joaquim Serra

We study stable solutions to the fractional Allen-Cahn equation \linebreak $(- Δ)^{s /2} u = u - u^{3}$ , $∣ u ∣ < 1$ in $R^{n}$ . For every $s \in (0, 1)$ and dimension $n \geq 2$ , we est…

math.AP2021

Interface regularity for semilinear one-phase problems

Alessandro Audrito, Joaquim Serra

We study critical points of a one-parameter family of functionals arising in combustion models. The problems we consider converge, for infinitesimal values of the parameter, to Ber…

math.AP2021

The singular set in the Stefan problem

Alessio Figalli, Xavier Ros-Oton, Joaquim Serra

In this paper we analyze the singular set in the Stefan problem and prove the following results: - The singular set has parabolic Hausdorff dimension at most $n - 1$ . - The solution…