Boundary expansions for minimal graphs in the hyperbolic space

Qing Han, Xumin Jiang

Published 2014-12-24Version 1

We study expansions near the boundary of solutions to the Dirichlet problem for minimal graphs in the hyperbolic space and characterize the remainders of the expansion by multiple integrals. With such a characterization, we establish optimal asymptotic expansions of solutions with boundary values of finite regularity and demonstrate a slight loss of regularity for nonlocal coefficients.