2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137964For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some system-dependent constant which is strictly less than 1 and, on the other hand, that for any system of the kind considered there is in fact a solution on a half-plane which fails to have nontangential limits at a set of boundary points of positive Hausdorff dimension.43 pages. This second version is largely the same as the first. The changes involve the correction of a number of errors, incorporation of some simplifications and more detailed proofs of a few of the propositionsAnalysis of PDEs35L40; 28A78text