Abstract
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.
Citation
Atsushi Nakayasu. Piotr Rybka. "Integrability of the derivative of solutions to a singular one-dimensional parabolic problem." Topol. Methods Nonlinear Anal. 52 (1) 239 - 257, 2018. https://doi.org/10.12775/TMNA.2018.031