Critical points of solutions of degenerate elliptic equations in the plane
Abstract
We study the minimizer u of a convex functional in the plane which is not G\ateaux-differentiable. Namely, we show that the set of critical points of any C1-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.
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