Spacelike graphs with prescribed mean curvature on exterior domains in the Minkowski spacetime

Abstract

We consider a Dirichlet problem for the mean curvature operator in the Minkowski spacetime, obtaining a necessary and sufficient condition for the existence of a spacelike solution, with prescribed mean curvature, which is the graph of a function defined on a domain equal to the complement in R n of the union of a finite number of bounded Lipschitz domains. The mean curvature H = H(x, t) is assumed to have absolute value controlled from above by a locally bounded, L p -function, p ∈ [1, 2n/(n + 2)], n ≥ 3.