Publications [#10219] of John B. Greer

Papers Accepted

1. John B. Greer and Andrea L. Bertozzi, H^1 Solutions of a Class of Fourth Order Nonlinear Equations for Image Processing, Journal of Discrete and Continuous Dynamical Systems , accepted 2002
   (last updated on 2002/07/23)

   Abstract:
   Recently fourth order equations of the form u_t = -\nabla\cdot(({\mathcal G}(J_\sigma u)) \nabla \Delta u) have been proposed for noise reduction and simplification of two dimensional images. The operator \mathcal G is a nonlinear functional involving the gradient or Hessian of its argument, with decay in the far field. The operator J_\sigma is a standard mollifier. Using ODE methods on Sobolev spaces, we prove existence and uniqueness of solutions of this problem for H^1 initial data.