Critical variable exponent functionals in image restoration

We study a variable exponent model for image restoration in the case that the exponent attains the critical value one. We prove existence and ΓΓ-convergence. The results answer an open question by Li, Li and Pi [F. Li, Z. Li, L. Pi, Ling, Variable exponent functionals in image restoration, Appl. Math. Comput. 216 (3) (2010) 870–882]