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- ItemNonlocal phase transitions: Rigidity results and anisotropic geometry(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Dipierro, Serena; Serra, Joaquim; Valdinoci, EnricoFinally, 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.
- ItemImprovement of flatness for nonlocal phase transitions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Dipierro, Serena; Serra, Joaquim; Valdinoci, EnricoWe prove an improvement of flatness result for nonlocal phase transitions. For a class of nonlocal equations, we obtain a result in the same spirit of a celebrated theorem of Savin for the classical case. The results presented are completely new even for the case of the fractional Laplacian, but the robustness of the proofs allows us to treat also more general, possibly anisotropic, integro-differential operators.
- ItemOn fractional elliptic equations in Lipschitz sets and epigraphs: Regularity, monotonicity and rigidity results(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Dipierro, Serena; Soave, Nicola; Valdinoci, EnricoWe 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 [4].