| Abstract: |
| We study the geometric and functional framework for a nonlocal Plateau problem with obstacles. In particular, we formulate the minimization of the fractional perimeter in cylinders with respect to graphical exterior data, as well as the equivalent variational problem for the nonlocal area functional. We then show that, when the prescribed exterior data is not too large at infinity and the fractional parameter is sufficiently small, minimizers exhibit complete stickiness: they adhere entirely to the obstacle and leave the remainder of the domain asymptotically empty. |
|