Abstract:This paper considers the Alt-Caffarelli free boundary problem in a periodic medium. This is a convenient model for several interesting phenomena appearing in the study of contact lines on rough surfaces, pinning, hysteresis and the formation of facets. We show the existence of an interval of effective pinned slopes at each direction e ∈ S d−1 . In d = 2 we characterize the regularity properties of the pinning interval in terms of the normal direction, including possible discontinuities at rational directions. … Show more
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