非光滑区域上含接触项泛函的松弛
On the relaxation of functionals with contact terms on non-smooth domains
摘要：
我们提供的整表示公式的松弛$BV(Ω; \mathbb{R}^M)$相对于强收敛$L^1(Ω; \mathbb{R}^M)$的功能与边界接触能量项。这种表征是有效的一个大类的表面能密度，并为域满足温和的规则性假设。出于一些经典的例子，下半连续性失败，我们分析了在何种程度上的几何集进入松弛过程。
英文摘要：
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.
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