Nonlocal Delaunay surfaces
- Davila, Juan
- del Pino, Manuel
- Dipierro, Serena
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35R11 49Q05 49Q20
- Delaunay surfaces, nonlocal perimeter, minimization problem
We construct codimension 1 surfaces of any dimension that minimize a nonlocal perimeter functional among surfaces that are periodic, cylindrically symmetric and decreasing. These surfaces may be seen as a nonlocal analogue of the classical Delaunay surfaces (onduloids). For small volume, most of their mass tends to be concentrated in a periodic array and the surfaces are close to a periodic array of balls (in fact, we give explicit quantitative bounds on these facts).
- Nonlinear Anal., 137 (2016) pp. 357--380.