2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155704We obtain a sharp local well-posedness result for the Gradient Nonlinear Wave Equation on a nonsmooth curved background. In the process we introduce variable coefficient versions of Bourgain's $X^{s,b}$ spaces, and use a trilinear multiscale wave packet decomposition in order to prove a key trilinear estimate.Analysis of PDEs35L70text