Metric Entropy for Functions of Bounded Total Generalized Variation
Metric Entropy for Functions of Bounded Total Generalized Variation
复制标题
有界总广义变分函数的度量熵
DOI：
10.1137/20m1310953
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
K. Nguyen
中科院分区：
文献类型：
--
作者：
R. Capuani;Prerona Dutta;K. Nguyen
我们建立了一个尖锐的估计的最小数量的二进制数字（位）需要表示所有有界的总广义变差函数采取的值在一般的全有界度量空间$（E，\rho）$到$\vareps>0$关于${\bfL}^1$-距离。这样的估计是显式计算的加倍和包装方面的尺寸$（E，\rho）$。所得结果应用于一维空间中具有弱真非线性通量的标量守恒律的熵容许弱解的度量熵的上界.
We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space $(E,\rho)$ up to an accuracy of $\varepsilon>0$ with respect to the ${\bf L}^1$-distance. Such an estimate is explicitly computed in terms of doubling and packing dimensions of $(E,\rho)$. The obtained result is applied to provide an upper bound on the metric entropy for a set of entropy admissible weak solutions to scalar conservation laws in one-dimensional space with weakly genuinely nonlinear fluxes.