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.
Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems
We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...
Superlinear elliptic systems with distributed and boundary controls