Voila une reference qui traite ce type de questions:

Z. Guo, Q. Liu, J. Sun, B. Wu, Reaction–diffusion systems with p(x)-growth for image denoising, Nonlinear Anal. RWA

12 (2011) 2904–2918.

Tu peux aussi voir ce papier: F. Karami, K. Sadik and L. Ziad. A variable exponent nonlocal p ( x ) -Laplacian equation for image restoration. Computers & Mathematics with Applications 75(2). 2017

Have a look at this reference:

Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth func-

tionals in image restoration, SIAM J. Appl. Math. 66, (2006), 1383-1406

I found on net an answer associated with previous answers, see this link: http://pcfm-ma.iecl.univ-lorraine.fr/communications/Sadik.pdf

best regards

Hellal Abdelaziz

M'sila, Algeria University

let's express our thanks for your answers