School of Mathematics and Statistics - Research Publications

Permanent URI for this collection

http://hdl.handle.net/11343/294

Filters

2017 2
Reset filters

Settings
Statistics
Citations
Start date: 2010 × End date: 2019 × Author: Valdinoci, Enrico × Author: Dipierro, Serena × Type: Journal Article ×

Search Results

Now showing 1 - 2 of 2
  • Item
    Thumbnail Image
    Nonlocal phase transitions in homogeneous and periodic media
    Cozzi, M ; Dipierro, S ; Valdinoci, E (SPRINGER BASEL AG, 2017-03)
    We discuss some results related to a phase transition model in which the potential energy induced by a double-well function is balanced by a fractional elastic energy. In particular, we present asymptotic results (such as $\Gamma$-convergence, energy bounds and density estimates for level sets), flatness and rigidity results, and the construction of planelike minimizers in periodic media. Finally, we consider a nonlocal equation with a multiwell potential, motivated by models arising in crystal dislocations, and we construct orbits exhibiting symbolic dynamics, inspired by some classical results by Paul Rabinowitz.
  • Item
    Thumbnail Image
    On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
    Dipierro, S ; Soave, N ; Valdinoci, E (Springer, 2017-12-01)
    We consider a nonlocal equation set in an unbounded domain with the epigraph property. We prove symmetry, monotonicity and rigidity results. In particular, we deal with halfspaces, coercive epigraphs and epigraphs that are flat at infinity. These results can be seen as the nonlocal counterpart of the celebrated article (Berestycki et al., Commun Pure Appl Math 50(11):1089–1111, 1997).