On shock generation for Hamilton-Jacobi equations

The subject of this paper is the generation of singularities of solutions of Hamilton-Jacobi equations set in (0, ∞) × ℝ fordataofclass C∞. Shockwaves originate from conjugate points. To show sharpness of a known Hausdorff estimate, an example is given in which the set of conjugate, regular points includes uncountably many affine subspaces of dimension n − 1.