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arXiv · 1912.00219

Metric entropy for functions of bounded total generalized variation

Rossana Capuani·Prerona Dutta·Khai T. Nguyen
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Abstract

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.

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BibTeXRIS

Rossana Capuani, Prerona Dutta, Khai T. Nguyen. 2019-11-30. Metric entropy for functions of bounded total generalized variation. https://arxiv.org/abs/1912.00219

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