Existence and behavior of the radial limits of a bounded capillary surface at a corner

Abstract

Consider a bounded capillary surface defined on a twodimensional region that has a corner point at 0, with opening angle 2a. If the contact angle is bounded away from 0 and , then the radial limits exist as 0 is approached from any direction in . If the contact angle approaches limiting values as 0 is approached along each portion of the boundary, then there exist "fans" of directions adjacent to the two tangent directions at 0 in which the radial limits are constant. Other properties of the radial limit function are given and these results are used to show continuity of the solution up to 0 under certain conditions. For a convex corner, the solution is continuous up to 0 when the limiting angles 7Q", 7^ satisfy fa" -7o" -7 < 2 and 2a + \*y -7^ < .