We study a nonlinear elliptic problem governed by a general Leray-Lions operator with variable exponents and diffuse Radon measure data that does not charge the sets of zero p(⋅)-capacity. We prove a decomposition theorem for these measures (more precisely, as a sum of a function in L1(Ω) and of a measure in W−1,p′(⋅)(Ω)) and an existence and uniqueness result of entropy solution.

diffuse measure; biting lemma of Chacon; maximal monotone graph; Radon measure data; weak solution; entropy solution; Leray-Lions operator