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arXiv math/04022872004-02-17math.CA

Lipschitz映射的凸积分与正则性的反例

Convex integration for Lipschitz mappings and counterexamples to regularity

S. Muller, V. Sverak

备注：: 28 pages published version
发表信息：: Ann. of Math. (2), Vol. 157 (2003), no. 3, 715--742

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摘要：

研究了偏微分关系$\nabla u\in K$的Lispchitz解，其中$u$是$R^n$的开子集上的向量值函数.在某些情况下，解的集合会大得惊人。然后利用一般理论构造了满足经典椭圆性条件的Euler-Lagrange方程组解的正则性的反例。

英文摘要：

We study Lispchitz solutions of partial differential relations $\nabla u\in K$, where $u$ is a vector-valued function in an open subset of $R^n$. In some cases the set of solutions turns out to be surprisingly large. The general theory is then used to construct counter-examples to regularity of solutions of Euler-Lagrange systems satisfying classical ellipticity conditions.

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