Weak convergence under nonlinearities
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| Format: | Artículo científico |
| Langue: | en |
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Academia Brasileira de Ciências
2003
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| _version_ | 1876428162574843904 |
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| author | Diego R. Moreira |
| author_facet | Diego R. Moreira |
| 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 |
| format | Artículo científico |
| id | redalyc_32775102 |
| institution | Redalyc |
| language | en |
| publishDate | 2003 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | Weak convergence under nonlinearities Diego R. Moreira Multidisciplinaria (Ciencias Naturales y Exactas) nonlinearities weak continuity Nemytskii operator 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 |
| title | Weak convergence under nonlinearities |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) nonlinearities weak continuity Nemytskii operator |
| url | https://www.redalyc.org/articulo.oa?id=32775102 |