论文标题
关于在非平滑域上具有接触术语的功能放松
On the relaxation of functionals with contact terms on non-smooth domains
论文作者
论文摘要
我们为$ l^1（ω; \ mathbb {r}^m）在$ bv（ω; \ mathbb {r}^m）$中提供放松的整体表示公式。这种表征对于大量的表面能密度和满足轻度规则假设的域是有效的。在某些经典的示例中，较低的半持续性失败的示例，我们分析了集合几何形状进入放松过程的程度。
We provide the integral representation formula for the relaxation in $BV(Ω; \mathbb{R}^M)$ with respect to strong convergence in $L^1(Ω; \mathbb{R}^M)$ of a functional with a boundary contact energy term. This characterization is valid for a large class of surface energy densities, and for domains satisfying mild regularity assumptions. Motivated by some classical examples where lower semicontinuity fails, we analyze the extent to which the geometry of the set enters the relaxation procedure.
