Renormalized solutions of p(x)-Laplace equations with an optional low order term

In the report, the existence of the renormalized solutions of the Dirichlet boundary conditions, which can be satisfied by p(x)-Laplace elliptic equations with an optional low order term in bounded domains Ω, was studied. The low order term H was optional, and which satisfied certain growth conditions, the right end item f belonged to L¹ data. The function space theory, the truncation functions, and the gradient estimation methods were used to prove the existence of the renormalization solutions for p(x)-Laplace equations.