Deville, RobertJaramillo Aguado, Jesús Ángel2023-06-202023-06-2020080213-223010.4171/RMI/564https://hdl.handle.net/20.500.14352/50121We study the existence of everywhere differentiable functions which are almost everywhere solutions of quite general Hamilton-Jacobi equations on open subsets of R(d) or on d-dimensional manifolds whenever d >= 2. In particular, when M is a Riemannian manifold, we prove the existence of a differentiable function a on M which satisfies the Eikonal equation parallel to del u(x)parallel to(x) = 1 almost everywhere on M.engjournal articlehttp://projecteuclid.org/euclid.rmi/1228834302http://projecteuclid.orgopen access517.55Riemannian-ManifoldsGradient ProblemHamilton-Jacobi EquationsEikonal Equation On ManifoldsAlmost Everywhere SolutionsMatemáticas (Matemáticas)Análisis matemáticoEcuaciones diferenciales12 Matemáticas1202 Análisis y Análisis Funcional1202.07 Ecuaciones en Diferencias