Convergence of convex sets with gradient constraint
Given a bounded open subset of R^N, we study the convergence of a sequence (K_n)_{n\in\N} of closed convex subsets of W_0^{1,p}(\Omega) (p\in]1,\infty[) with gradient constraint, to a convex set K, in the Mosco sense. A particular case of the problem studied is when K_n={v\in W_0^{1,p}(\Omega):: F_n...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | article |
| Language: | eng |
| Published: |
2004
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1822/2899 |
| Country: | Portugal |
| Oai: | oai:repositorium.sdum.uminho.pt:1822/2899 |
| Summary: | Given a bounded open subset of R^N, we study the convergence of a sequence (K_n)_{n\in\N} of closed convex subsets of W_0^{1,p}(\Omega) (p\in]1,\infty[) with gradient constraint, to a convex set K, in the Mosco sense. A particular case of the problem studied is when K_n={v\in W_0^{1,p}(\Omega):: F_n(x,\nabla v(x))<= g_n(x) for a.e. x in \Omega}. Some examples of non-convergence are presented. We also present an improvement of a result of existence of a solution of a quasivariational inequality, as an application of this Mosco convergence result. |
|---|