Convergence relation between p(x)-harmonic maps and minimizers of p(x)-energy functional with penalization

We prove that the p(x)-Ginzburg–Landau type minimizers converge to the p(x)-harmonic maps. The location of zeros of the minimizers is presented in the case of p(x)∈(1,2). When p(x)>2, there exists no zero of the minimizers in the domain. In addition, the convergence rate of the modulus of the minimizers to 1 is estimated.