J. Serra

activity

20112023

s

-minimal cones in

R^{3}

are flat for

s \sim 1

4 citations · 8 across the 8 of their papers we have counts for

collaborators

Showing 2017Show all

3 papers · 1 filter

math.AP2017★ 4 cited

Stable $s$ -minimal cones in $R^{3}$ are flat for $s \sim 1$

Xavier Cabre, Eleonora Cinti, Joaquim Serra

We prove that half spaces are the only stable nonlocal $s$ -minimal cones in $R^{3}$ , for $s \in (0, 1)$ sufficiently close to $1$ . This is the first classification result of st…

math.AP2017

On the fine structure of the free boundary for the classical obstacle problem

Alessio Figalli, Joaquim Serra

In the classical obstacle problem, the free boundary can be decomposed into "regular" and "singular" points. As shown by Caffarelli in his seminal papers \cite{C77,C98}, regular po…

math.AP2017

On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1

Alessio Figalli, Joaquim Serra

We prove that every bounded stable solution of \[ (-Δ)^{1/2} u + f(u) =0 \qquad \mbox{in }\mathbb R^3\] is a 1D profile, i.e., $u (x) = ϕ (e \cdot x)$ for some $e \in S^{2}$ , wher…

Stable s-minimal cones in R3 are flat for s∼1

On the fine structure of the free boundary for the classical obstacle problem

On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1

Stable $s$ -minimal cones in $R^{3}$ are flat for $s \sim 1$