Local solutions to Darboux problem with a discontinuous right-hand side - Pikuta, P. (Condensed Matter Physics, 2008)
The existence of a local solution to the Darboux problem uxy (x, y) = g (u (x, y)), u (x, 0) = u (0, y) = 0, where g is Lebesgue measurable and has at most polynomial growth, is proved.