Abstract
We consider the prescribed mean curvature problem of spacelike graphs in Robertson- Walker spacetimes of flat fiber with homogeneous Dirichlet conditions on an Euclidean ball. Under reasonable assumptions, it is shown that every possible solution must be radially symmetric. Besides, an existence result for a singular nonlinear equation is proved by making use of the classical Schauder fixed point Theorem. The results are applied to realistic examples of Robertson-Walker spacetimes.
Keywords: Dirichlet boundary problem; prescribed mean curvature function; Robertson-Walker spacetime; singular nonlinear equation
Received: 2014-04-04
Published Online: 2016-03-10
Published in Print: 2015-02-01
© 2016 by Advanced Nonlinear Studies, Inc.
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