BV SOLUTIONS TO A DEGENERATE PARABOLIC EQUATION FOR IMAGE DENOISING

In this article, the authors consider equation ut = div（φ（Γu）A（｜Du｜^2）Du） - （u- I）, where φ is strictly positive and F is a known vector-valued mapping, A ： R＋ → R^＋ is decreasing and A（s） -1/ √s as s → ＋∞. This kind of equation arises naturally from image denoising. For an initial datum I ∈ BVloc ∩ L^∞, the existence of BV solutions to the initial value problem of the equation is obtained.