A density result for doubly nonlinear operators in $ L^1 $.

The aim of this paper is to provide sufficient conditions implying that the effective domain $ D(A\phi) $ of an $ m $-accretive operator $ A\phi $ in $ L^1 $ is dense in $ L^1 $. Here, $ A\phi $ refers to the composition $ A\circ \phi $ in $ L^1 $ of the part $ A = (\partial\mathcal{E})_{\vert L^{1\cap \infty}} $ in $ L^{1\cap\infty} $ of the subgradient $ \partial\mathcal{E} $ in $ L^2 $ of a convex, proper, lower semicontinuous functional $ \mathcal{E} $ on $ L^2 $ and a continuous, strictly increasing function $ \phi $ on the real line $ \mathbb{R} $. To illustrate the role of the sufficient conditions, we apply our main result to the class of doubly nonlinear operators $ A\phi $, where $ A $ is a classical Leray-Lions operator. [ABSTRACT FROM AUTHOR]