Critical points of solutions of degenerate elliptic equations in the plane

Details Critical points of solutions of degenerate elliptic equations in the plane Critical points of solutions of degenerate elliptic equations in the plane

2008-12-22

arxiv.org/abs/0812.4244v1

Mathematics

Analysis of PDEs

1 figure

Scientific paper

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 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.

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