论文标题
最佳$ c^\ infty $ - 用指数或亚指数的拟态性派生的功能
Optimal $C^\infty$-approximation of functions with exponentially or sub-exponentially integrable derivative
论文作者
论文摘要
我们讨论了Meyers-Serrin的类型结果，以进行函数平滑近似$ B = B = B（T，X）：\ Mathbb {R} \ Times \ Times \ MathBb {R}^n \ to \ Mathbb {r}^m $，并带有形式的能量\ [ \ int _ {\ Mathbb {r}} \ int _ {\ Mathbb {r}^n} $φ：[0，\ infty）\ to [0，\ infty）$是一个凸功能，其$φ（0）= 0 $具有指数级或亚指数增长。
We discuss Meyers-Serrin's type results for smooth approximations of functions $b=b(t,x):\mathbb{R}\times\mathbb{R}^n\to\mathbb{R}^m$, with convergence of an energy of the form \[ \int_{\mathbb{R}}\int_{\mathbb{R}^n} w(t,x) φ\left(|Db(t,x)|\right)\mathrm{d} x \mathrm{d} t\,, \] where $w>0$ is a suitable weight function, and $φ:[0,\infty)\to [0,\infty)$ is a convex function with $φ(0)=0$ having exponential or sub-exponential growth.
