Integrability of the derivative of solutions to a singular one-dimensional parabolic problem
Integrability of the derivative of solutions to a singular one-dimensional parabolic problem
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 …