Integrability of the derivative of solutions to a singular one-dimensional parabolic problem. (English) Zbl 1407.35120
Summary: 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.
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