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Existence of solutions of the Capillary problem in $M\times\mathbb{R}$

Universidad Autónoma de Madrid

The capillary problem considers an interface separating two fluids that lie adjacent to each other and do not mix. This imposes certain geometric conditions on the interface surface and its boundary. The existence, uniqueness and regularity of such surfaces has been widely studied in Rn. Here we study the existence of a graph in MxR with prescribed mean curvature and prescribed contact angle, where M is a Riemannian manifold. We follow the work of Korevaar to estimate the gradient of solutions, using the maximum principle. This is joint work with Leili Shariyari.

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