Toward a Long-Range Theory of Capillarity

We recall the classical theory of capillarity, describing the shape<br/>of a liquid droplet in a container, and present a recent approach<br/>which aims at accounting for long-range particle interactions.<br/>This nonlocal setting recovers the classical notion of surface<br/>tension in the limit. We provide some regularity results and<br/>the determination of the contact angle, supplied with various<br/>asymptotics.