Critical points of solutions of degenerate elliptic equations in the plane

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We 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.
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Analysis of PDEs, 35B05, 35B38, 35J20, 35J60

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http://salesiana.dossiersoluciones.com/handle/123456789/213313

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0812.4244
 http://arxiv.org/abs/0812.4244

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arXiv