2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213313We study the minimizer u of a convex functional in the plane which is not Gâteaux-differentiable. Namely, we show that the set of critical points of any C^1-smooth minimizer can not have isolated points. Also, by means of some appropriate approximating scheme and viscosity solutions, we determine an Euler-Lagrange equation that u must satisfy. By applying the same approximating scheme, we can pair u with a function v which may be regarded as the stream function of u in a suitable generalized sense.1 figureAnalysis of PDEs35B05, 35B38, 35J20, 35J60text