@article{capuani_dutta_nguyen_2021, title={METRIC ENTROPY FOR FUNCTIONS OF BOUNDED TOTAL GENERALIZED VARIATION}, volume={53}, ISSN={["1095-7154"]}, url={http://dx.doi.org/10.1137/20m1310953}, DOI={10.1137/20M1310953}, abstractNote={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.}, number={1}, journal={SIAM JOURNAL ON MATHEMATICAL ANALYSIS}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Capuani, Rossana and Dutta, Prerona and Nguyen, Khai T.}, year={2021}, pages={1168–1190} }
 @article{dutta_nguyen_2018, title={Covering numbers for bounded variation functions}, volume={468}, ISSN={0022-247X}, url={http://dx.doi.org/10.1016/j.jmaa.2018.08.062}, DOI={10.1016/j.jmaa.2018.08.062}, abstractNote={In this paper, we provide upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to L1-distance.}, number={2}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Dutta, Prerona and Nguyen, Khai T.}, year={2018}, month={Dec}, pages={1131–1143} }