A Class Of Elliptic Equations with Interior Degeneration
  A class of linear degenerate elliptic equations inspired by nonlinear diffusions of image processing is considered. It is characterized by an interior degeneration of the diffusion coefficient. It is shown that no particularly natural, unique interpretation of the equation is possible. This phenomenon is reflected in the behavior of numerical schemes for its resolution and points to similar issues that potentially affect its nonlinear counterpart. 
Patrick Guidotti
math.AP