On a quasilinear degenerated elliptic unilateral problems with $$L^1$$ data

Entropy and renormalized solutions for some nonlinear anisotropic elliptic equations with variable exponents and L 1-data

“…For the corresponding isotropic parabolic equations with L 1 -data, existence and uniqueness of renormalized solutions is established in Blanchard and Murat [22], see also Rakotoson [38,39] and Lions [37] for some time dependent problems motivated by the Navier-Stokes equations. Finally, let us mention that an equivalent notion of solutions, called entropy solutions, was introduced independently by Bénilan et al [15], see also [11], several researches deals with the existence solutions of elliptic and parabolic problems under various assumptions and in different contexts (see [42,32,43,6,8,19,1,7,5,2,16,9,17,20,3,10,4,18,30,31,29,25,21]).…”

Entropy solutions for nonlinear parabolic equations in Musielak Orlicz spaces without Delta_2-conditions

“…A large number of research deals with existence solutions of elliptic and parabolic problems under different assumptions in order to get a classical results see [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,25,26,27,28,31,37,42,43] for more details.…”