Math @ Duke

Publications [#10219] of John B. Greer
Papers Accepted
 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 [ps]
(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.


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