@article {IOPORT.06106996, author = {Harjulehto, P. and H\"ast\"o, P. and Latvala, V. and Toivanen, O.}, title = {Critical variable exponent functionals in image restoration.}, year = {2013}, journal = {Applied Mathematics Letters}, volume = {26}, number = {1}, issn = {0893-9659}, pages = {56-60}, publisher = {Elsevier Science Ltd. (Pergamon), Oxford}, doi = {10.1016/j.aml.2012.03.032}, abstract = {Summary: We study a variable exponent model for image restoration in the case that the exponent attains the critical value one. We prove existence and $\Gamma $-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]}, identifier = {06106996}, }