Density of convex intersections and applications
- Hintermüller, Michael
- Rautenberg, Carlos N.
- Rösel, Simon
2010 Mathematics Subject Classification
- 97N40 46E35 65K15 35J86 65N30 74C15 94A08
- Density, convex constraints, variational inequalities, finite elements, image restoration, elasto-plasticity
In this paper we address density properties of intersections of convex sets in several function spaces. Using the concept of Gamma-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite element discretizations of sets associated to convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems.
- Proc. Roy. Soc. Edinburgh Sect. A, 473 (2017), pp. 20160919/1--20160919/28, DOI 10.1098/rspa.2016.0919 .