Gradient estimates for the Perona-Malik equation Marina Ghisi

@inproceedings{Ghisi2006GradientEF,
  title={Gradient estimates for the Perona-Malik equation Marina Ghisi},
  author={Marina Ghisi and Massimo Gobbino},
  year={2006}
}
We consider the Cauchy problem for the Perona-Malik equation ut = div ( ∇u 1 + |∇u|2 ) in a bounded open set Ω ⊆ R, with Neumann boundary conditions. If n = 1, we prove some a priori estimates on u and ux. Then we consider the semi-discrete scheme obtained by replacing the space derivatives by finite differences. Extending the previous estimates to the… CONTINUE READING