Solutions of the divergence operator on John domains
If Ω ⊂ Rn is a bounded domain, the existence of solutions u ∈ W01, p (Ω) of div u = f for f ∈ Lp (Ω) with vanishing mean value and 1 < p < ∞, is a basic result in the analysis of the Stokes equations. It is known that the result holds when Ω is a Lipschitz domain and that it is not valid for d...
Guardado en:
| Autores principales: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2005
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/83153 |
| Aporte de: |
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I19-R120-10915-83153 |
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| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Ciencias Exactas Divergence operator John domains Singular integrals |
| spellingShingle |
Ciencias Exactas Divergence operator John domains Singular integrals Acosta, Gabriel Durán, Ricardo G. Muschietti, María Amelia Solutions of the divergence operator on John domains |
| topic_facet |
Ciencias Exactas Divergence operator John domains Singular integrals |
| description |
If Ω ⊂ Rn is a bounded domain, the existence of solutions u ∈ W01, p (Ω) of div u = f for f ∈ Lp (Ω) with vanishing mean value and 1 < p < ∞, is a basic result in the analysis of the Stokes equations. It is known that the result holds when Ω is a Lipschitz domain and that it is not valid for domains with external cusps. In this paper we prove that the result holds for John domains. Our proof is constructive: the solution u is given by an explicit integral operator acting on f. To prove that u ∈ W01, p (Ω) we make use of the Calderón-Zygmund singular integral operator theory and the Hardy-Littlewood maximal function. For domains satisfying the separation property introduced in [S. Buckley, P. Koskela, Sobolev-Poincaré implies John, Math. Res. Lett. 2 (5) (1995) 577-593], and 1 < p < n, we also prove a converse result, thus characterizing in this case the domains for which a continuous right inverse of the divergence exists. In particular, our result applies to simply connected planar domains because they satisfy the separation property. |
| format |
Articulo Articulo |
| author |
Acosta, Gabriel Durán, Ricardo G. Muschietti, María Amelia |
| author_facet |
Acosta, Gabriel Durán, Ricardo G. Muschietti, María Amelia |
| author_sort |
Acosta, Gabriel |
| title |
Solutions of the divergence operator on John domains |
| title_short |
Solutions of the divergence operator on John domains |
| title_full |
Solutions of the divergence operator on John domains |
| title_fullStr |
Solutions of the divergence operator on John domains |
| title_full_unstemmed |
Solutions of the divergence operator on John domains |
| title_sort |
solutions of the divergence operator on john domains |
| publishDate |
2005 |
| url |
http://sedici.unlp.edu.ar/handle/10915/83153 |
| work_keys_str_mv |
AT acostagabriel solutionsofthedivergenceoperatoronjohndomains AT duranricardog solutionsofthedivergenceoperatoronjohndomains AT muschiettimariaamelia solutionsofthedivergenceoperatoronjohndomains |
| bdutipo_str |
Repositorios |
| _version_ |
1764820488341684225 |