Abstract :
In this paper, we obtain the following local weighted Lorentz gradient estimates g−1(M1(μ))∈Lq,rw,loc(Ω)⟹|Du|∈Lq,rw,loc(Ω) for the weak solutions of a class of non-homogeneous quasilinear elliptic equations with measure data −div (a(|∇u|)∇u)=μ, where g(t)=ta(t) for t≥0 and M1(μ)(x):=supr 0r|μ|(Br(x))/|Br(x)|,x∈Rn. Moreover, we remark that two natural and simple examples of functions g(t) in this work are g(t)=tp−1 (p-Laplace equation) and g(t)=tp−1logα(1+t) for α 0. Actually, the more general and interesting example is related to (p, q)-growth condition by appropriate gluing of the monomials. We remark that our results improve the known results for such equations.
