In this paper, we study a suitable notion of solution for which a nonlinear elliptic problem governed by a general Leray–Lions operator is well posed for any diffuse measure data. In terms of the paper (Brezis et al., 2007, [10]), we study the notion of solution for which any diffuse measure is “good measure”.

Nonlinear elliptic, Diffuse measure, Biting lemma of Chacon, Maximal monotone graph, Radon measure data, Weak solution, Entropic solution, Leray–Lions operator