期刊
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
卷 39, 期 1-2, 页码 121-138出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-009-0304-8
关键词
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We study the minimizer u of a convex functional in the plane which is not Gateaux-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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