| Abstract: |
| In this talk, we consider gradient systems of non-convex functionals, defied by integrals on a bounded spatial domain $ \Omega \subset \mathbb{R}^2 $. Each functional is based on a governing energy for anisotropic image processing, proposed by [Berkels et -al, pp. 293--301, Vision Modeling and Visualization 2006 (2006)], and the principal part of the corresponding gradient system is descried in a nonstandard form of \emph{partial differential inclusions}, which contains a composition $ \partial \gamma \circ R $ of: a (possibly) set-valued subdifferential $ \partial \gamma $ of an anisotropic metric $ \gamma \in W^{1, \infty}(\mathbb{R}^2) $; and a rotation matric $ R \in C^\infty(\mathbb{R}; \mathbb{R}^{2 \times 2}) $. Under appropriate assumptions, some mathematical observations for the gradient system will be provided on the basis of the time-discretization approach. |
|