On time flows of minimizers of general convex functionals of linear growth with variable exponent in BV space and stability of pseudosolutions

Here we examine a method of selective smoothing in image restoration in BV space using a variable exponent functional of linear growth. Variable exponent growth was suggested in P. Blomgren et al. (1997) [6], and in Y. Chen et al. (2006) [8] the notion of a pseudosolution of the minimization problem is discussed, as well as the proof of existence and uniqueness of the solution of the time flow for the associated time dependent PDE. Here we prove stability for pseudosolutions, while also discussing the case for more general convex functionals of linear growth and variable exponent for use as an approximation for the time flow other than that which is used in Y. Chen et al. (2006) [8].