@article{Nakayasu_Rybka_2018, title={Integrability of the derivative of solutions to a singular one-dimensional parabolic problem}, volume={52}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2018.031}, abstractNote={We study integrability of the derivative of a solution to a singular one-dimensional parabolic equation with initial data in $W^{1,1}$. In order to avoid additional difficulties we consider only the periodic boundary conditions. The problem we study is a gradient flow of a convex, linear growth variational functional. We also prove a similar result for the elliptic companion problem, i.e.\ the time semidiscretization.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={Nakayasu, Atsushi and Rybka, Piotr}, year={2018}, month={Aug.}, pages={239–257} }