Some properties of capillary surfaces (Q1878644)

The author describes a number of interesting mathematical results that relate to physical phenomena associated with capillarity. Some of these results predict discontinuous dependence on data due to certain nonlinearity of the underlying equations. Some of the predictions offer a strong support to the view that the equations are basically correct as descriptions of physical reality, since they have been tested experimentally. The aim of the paper is also to draw attention to some important unsolved problems.