APPROXIMATING ANNULAR CAPILLARY SURFACES WITH EQUAL CONTACT ANGLES

摘要

Consider an annular region Omega x R~2. We extend the iterative procedure of Siegel to the case of symmetric capillary surfaces z = u(x, y) formed within the annular cylinder Omega x R and having identical contact angles gamma along the inner and outer boundaries. We demonstrate convergence under conditions that include gamma = 0, and we recover the interleaving properties noted by Siegel for a particular geometry.