Saved in:
| Main Author: | |
|---|---|
| Format: | Artículo científico |
| Language: | en |
| Published: |
Academia Brasileira de Ciências
2003
|
| Subjects: | |
| Online Access: | https://www.redalyc.org/articulo.oa?id=32775102 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Weak convergence under nonlinearities Diego R. Moreira Eduardo V. O. Teixeira Multidisciplinaria (Ciencias Naturales y Exactas) nonlinearities weak continuity Nemytskii operator In this paper, we prove that if a Nemytskii operator maps Lp(W, E) into Lq(W, F), for p, q greater than 1, E, F separable Banach spaces and F reflexive, then a sequence that converge weakly and a.e. is sent to a weakly convergent sequence. We give a counterexample proving that if q = 1 and p is greater than 1 we may not have weak sequential continuity of such operator. However, we prove that if p = q = 1, then a weakly convergent sequence that converges a.e. is mapped into a weakly convergent sequence by a Nemytskii operator. We show an application of the weak continuity of the Nemytskii operators by solving a nonlinear functional equation on W1,p(W), providing the weak continuity of some kind of resolvent operator associated to it and getting a regularity result for such solution. 2003 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32775102 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.1 Vol.75