Solvability of boundary value problems for operator-differential equations of mixed type.
Some insights into the regularization of ill-posed problems.
Structural properties of solutions to total variation regularization problems
Structural Properties of Solutions to Total Variation Regularization Problems
In dimension one it is proved that the solution to a total variation-regularized least-squares problem is always a function which is "constant almost everywhere" , provided that the data are in a certain sense outside the range of the operator to be inverted. A similar, but weaker result is derived in dimension two.