| Registro completo |
| Provedor de dados: |
Anais da ABC (AABC)
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| País: |
Brazil
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| Título: |
Weak convergence under nonlinearities
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| Autores: |
MOREIRA,DIEGO R.
TEIXEIRA,EDUARDO V. O.
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| Data: |
2003-03-01
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| Ano: |
2003
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| Palavras-chave: |
Weak continuity
Nonlinearities
Nemytskii operator
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| Resumo: |
In this paper, we prove that if a Nemytskii operator maps Lp(omega, E) into Lq(omega, 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(omega), providing the weak continuity of some kind of resolvent operator associated to it and getting a regularity result for such solution.
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| Tipo: |
Info:eu-repo/semantics/article
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| Idioma: |
Inglês
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| Identificador: |
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652003000100002
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| Editor: |
Academia Brasileira de Ciências
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| Relação: |
10.1590/S0001-37652003000100002
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| Formato: |
text/html
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| Fonte: |
Anais da Academia Brasileira de Ciências v.75 n.1 2003
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| Direitos: |
info:eu-repo/semantics/openAccess
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