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We study "heavy" A?-dimensional surfaces suspended from some prescribed (n — 1) -dimensional boundary data. This leads to a mean curvature type equation with a non-monotone right hand side. We show that the equation has no solution if the boundary data are too small, and, using a fixed point argument, that the problem always has a smooth solution for sufficiently large boundary data. Consider a material surface M of constant mass density which is suspended from an (n - 1 )-dimensional surface Γ in Rn x R+, R+ = {t > 0}, and hangs under its own weight. If M is given as graph of a regular function u: Ω —• R + on a domain Ω c Rw, n > 2, then u provides an equilibrium for the potential energy g7 under gravitational forces, = ί JΩ \Du\ Ω V Thus u solves the Dirichlet problem

Then-dimensional analogue of the catenary: existence and nonexistence