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)ut=div(φ(Γu)A(|Du|2)Du)-(u-I), where φ is strictly positive and Γ is a known vector-valued mapping, A:ℝ+→ℝ+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∈BVioc∩L∞I∈BVioc∩L∞, the existence of BV solutions to the initial value problem of the equation is obtained.