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Variational methods and applications

Flatness results for stable solutions to some nonlocal problems

speaker: Eleonora Cinti (Università di Bologna)

abstract: We study stable solutions to two, closely related, nonlocal problems: the fractional minimal surfaces equation and the fractional Allen-Cahn equation. In particular, we establish optimal energy estimates, whose local analogue is still unknown. These estimates, together with other ingredients (such as density estimates and a monotonicity formula) allow to prove flatness of level sets. These results have been obtained in collaboration with X. Cabré, J. Serra, and E. Valdinoci.

timetable:
Thu 9 Sep, 9:30 - 10:20, Aula Dini
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