Convergence of solutions to the $p$-Laplace evolution equation as $p$   goes to 1
  We prove that the set of solutions to the parabolic singular $p$-Laplace equation with Dirichlet boundary conditions on a bounded Lipschitz domain $\Omega$ for all space dimensions is continuous in the parameter $p\in [1,+\infty)$ and the initial data. The highly singular limit case p=1 is included. In particular, we show that the solutions $u_p$ converge strongly in $L^2(\Omega)$, uniformly in time, to the solution $u_1$ of the parabolic 1-Laplace equation as $p\to 1$. 
Jonas M. T\"olle
math.AP math.OC