169 research outputs found
Regularity properties of nonlocal minimal surfaces via limiting arguments
We prove an improvement of flatness result for nonlocal minimal surfaces
which is independent of the fractional parameter when .
As a consequence, we obtain that all the nonlocal minimal cones are flat and
that all the nonlocal minimal surfaces are smooth when the dimension of the
ambient space is less or equal than 7 and is close to 1
Random homogenization of an obstacle problem
We study the homogenization of an obstacle problem in a perforated domain.
The holes are periodically distributed but have random size and shape. The
capacity of the holes is assumed to be stationary ergodic. As in the periodic
case, we show that the asymptotic behavior of the solutions is described by an
elliptic equation involving an additional term that takes into account the
effects of the obstacle.Comment: 28 page
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