Nonlocal phase transitions: Rigidity results and anisotropic geometry
- Dipierro, Serena
- Serra, Joaquim
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35R11 60G22 82B26
- nonlocal phase transitions, rigidity results, sliding methods
We provide a series of rigidity results for a nonlocal phase transition equation. The results that we obtain are an improvement of flatness theorem and a series of theorems concerning the one-dimensional symmetry for monotone and minimal solutions, in the research line dictaded by a classical conjecture of E. De Giorgi. Here, we collect a series of pivotal results, of geometric type, which are exploited in the proofs of the main results in a companion paper.