Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/48041
Título: | Lagrange multipliers and transport densities |
Autor(es): | Azevedo, Assis Santos, Lisa |
Palavras-chave: | Elliptic quasilinear equations Lagrange multipliers Non-constant gradient constraints |
Data: | 1-Out-2017 |
Editora: | Elsevier Masson |
Revista: | Journal de Mathématiques Pures et Appliquées |
Resumo(s): | In this paper we consider a stationary variational inequality with nonconstant gradient constraint and we prove the existence of solution of a Lagrange multiplier, assuming that the bounded open not necessarily convex set O has a smooth boundary. If the gradient constraint g is sufficiently smooth and satisfies ?g 2 =0 and the source term belongs to L 8 (O), we are able to prove that the Lagrange multiplier belongs to L q (O), for 1 < q < 8, even in a very degenerate case. Fixing q=2, the result is still true if ?g 2 is bounded from above by a positive sufficiently small constant that depends on O, q, minO??g and maxO??g. Without the restriction on the sign of ?g 2 we are still able to find a Lagrange multiplier, now belonging to L 8 (O) ' . We also prove that if we consider the variational inequality with coercivity constant d and constraint g, then the family of solutions (? d ,u d ) d > 0 of our problem has a subsequence that converges weakly to (? 0 ,u 0 ), which solves the transport equation. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/48041 |
DOI: | 10.1016/j.matpur.2017.05.004 |
ISSN: | 0021-7824 |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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AzevedoSantos_Lagrange_multipliers_RepositoriUM.pdf | 366,9 kB | Adobe PDF | Ver/Abrir |