On the solutions to 1-Laplacian equation with L~1 data

摘要

In the present paper we study the behaviour, as p goes to 1, of the renormalized solutions to the problems where p > 1,Ω is a bounded open set of 1R (N 2) with Lipschitz boundary and f belongs to L~1(Ω). We prove that these renormalized solutions pointwise converge, up to "subsequences," to a function u. With a suitable definition of solution we also prove that u is a solution to a "limit problem." Moreover we analyze the situation occurring when more regular data f are considered.