Abstract

I will introduce my recent work with my advisor Will Feldman on the homogenization of a parabolic equation with its Neumann condition oscillating in the "vertical" u-variable. The resulting PDE shows a novel singular anisotropic pinned Neumann condition, which involves an emerging free boundary. I will explain the technique and its connection to capillary droplet motions on rough surfaces and other free boundary problems. I will also highlight some open problems.