Existence of smooth solutions to a one-dimensional nonlinear degenerate variational wave equation

This paper is focused on a one-dimensional nonlinear variational wave equation which is the Euler-Lagrange equations of a variational principle arising in the theory of nematic liquid crystals and a few other physical contexts. We establish the global existence of smooth solutions to its degenerate initial-boundary value problem under relaxed conditions on the initial-boundary data. Moreover, we show that the solution is uniformly C1,α continuous up to the degenerate boundary and the degenerate curve is C1,α continuous for α∈(0,12).