Regularity of capillary surfaces over domains with corners
Leon Simon · Pacific Journal of Mathematics · 1980
Using the usual mathematical model (capillary surface equation with contact angle boundary condition) we discuss regularity of the equilibrium free surface of a fluid in a cylindrical container in case the container cross-section has corners.It is shown that good regularity holds at a corner if the "corner angle" θ satisfies Oττ, where 0</3< π/2 is the contact angle between the fluid surface and the container wall.It is known that no regularity holds in case θ + 2β<π, hence only the borderline case θ + 2β = π remains open.