Relaxation of signed integral functionals in BV
Relaxation of signed integral functionals in BV
复制标题
BV 中带符号积分泛函的松弛
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
F. Rindler
中科院分区：
文献类型：
--
作者：
Jan Kristensen;F. Rindler
For integral functionals initially defined for $${u \in {\rm W}^{1,1}(\Omega; \mathbb{R}^m)}$$ by$$\int_{\Omega} f(\nabla u) \, {\rm d}x$$we establish strict continuity and relaxation results in $${{\rm BV}(\Omega; \mathbb{R}^m)}$$ . The results cover the case of signed continuous integrands $${f : \mathbb{R}^{m \times d} \to \mathbb{R}}$$ of linear growth at infinity. In particular, it is not excluded that the integrands are unbounded below.
For integral functionals initially defined for $${u \in {\rm W}^{1,1}(\Omega; \mathbb{R}^m)}$$ by$$\int_{\Omega} f(\nabla u) \, {\rm d}x$$we establish strict continuity and relaxation results in $${{\rm BV}(\Omega; \mathbb{R}^m)}$$ . The results cover the case of signed continuous integrands $${f : \mathbb{R}^{m \times d} \to \mathbb{R}}$$ of linear growth at infinity. In particular, it is not excluded that the integrands are unbounded below.