论文标题
简化的反示例对双重积分的放松的积分表示
A simplified counterexample to the integral representation of the relaxation of double integrals
论文作者
论文摘要
我们表明，非凸双积分的较低连续包膜可能不允许表示表示为双积分。通过使用一个带有Value $+\ infty $的intandand，除了三分（例如$ -1 $，$ 0 $和$ 1 $）以外，我们给出了一个简单的证明和一个明确的放松公式，希望可以对这种类型的问题有所了解。这是Mora-Corral和Tellini的简化示例，以及Kreisbeck和Zappale，他们通过年轻措施来表征较低的连续性信封。
We show that the lower-semicontinuous envelope of a non-convex double integral may not admit a representation as a double integral. By taking an integrand with value $+\infty$ except at three points (say $-1$, $0$ and $1$) we give a simple proof and an explicit formula for the relaxation that hopefully may shed some light on this type of problems. This is a simplified version of examples by Mora-Corral and Tellini, and Kreisbeck and Zappale, who characterize the lower-semicontinuous envelope via Young measures.
