Metric Entropy for Functions of Bounded Total Generalized Variation
Copyright policy )Metric Entropy for Functions of Bounded Total Generalized Variation
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 $(E,��)$ 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 $(E,��)$. 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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- North Carolina State University United States
- University of Verona Italy
- South Carolina State University United States
- NORTH CAROLINA STATE UNIVERSITY United States
- North Carolina Agricultural and Technical State University United States
sharp estimate for a minimal number of binary digits, doubling dimension, metric entropy, Approximation by other special function classes, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Hyperbolic conservation laws, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), First-order hyperbolic equations, total generalized variation, Analysis of PDEs (math.AP)
sharp estimate for a minimal number of binary digits, doubling dimension, metric entropy, Approximation by other special function classes, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Hyperbolic conservation laws, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), First-order hyperbolic equations, total generalized variation, Analysis of PDEs (math.AP)
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