Quasi-Newton minimization for the p(x)p(x)-Laplacian problem

We propose a quasi-Newton minimization approach for the solution of the p(x)p(x)-Laplacian elliptic problem, x∈Ω⊂Rmx∈Ω⊂Rm. This method outperforms those existing for the p(x)p(x)-variable case, which are based on general purpose minimizers such as BFGS. Moreover, when compared to ad hoc   techniques available in literature for the pp-constant case, and usually referred to as “mesh independent”, the present method turns out to be generally superior thanks to better descent directions given by the quadratic model.