Convergence relation between -harmonic maps and minimizers of -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.