Optimal boundary holes for the Sobolev trace constant
In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ∥u∥W1,p(ω)p/∥u∥Lq(∂ω)p among functions that vanish in a set contained on the boundary ∂ ω of given boundary measure.We prove existence of extremals for this problem, and analyze some particular cases where informati...
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| Formato: | Artículo publishedVersion |
| Lenguaje: | Inglés |
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2011
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00220396_v251_n8_p2327_DelPezzo |
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paperaa:paper_00220396_v251_n8_p2327_DelPezzo2023-06-12T16:43:40Z Optimal boundary holes for the Sobolev trace constant J. Differ. Equ. 2011;251(8):2327-2351 Del Pezzo, L. Fernández Bonder, J. Neves, W. P-Laplace operator Shape optimization Steklov eigenvalues In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ∥u∥W1,p(ω)p/∥u∥Lq(∂ω)p among functions that vanish in a set contained on the boundary ∂ ω of given boundary measure.We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set. © 2011 Elsevier Inc. Fil:Del Pezzo, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00220396_v251_n8_p2327_DelPezzo |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
P-Laplace operator Shape optimization Steklov eigenvalues |
| spellingShingle |
P-Laplace operator Shape optimization Steklov eigenvalues Del Pezzo, L. Fernández Bonder, J. Neves, W. Optimal boundary holes for the Sobolev trace constant |
| topic_facet |
P-Laplace operator Shape optimization Steklov eigenvalues |
| description |
In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ∥u∥W1,p(ω)p/∥u∥Lq(∂ω)p among functions that vanish in a set contained on the boundary ∂ ω of given boundary measure.We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set. © 2011 Elsevier Inc. |
| format |
Artículo Artículo publishedVersion |
| author |
Del Pezzo, L. Fernández Bonder, J. Neves, W. |
| author_facet |
Del Pezzo, L. Fernández Bonder, J. Neves, W. |
| author_sort |
Del Pezzo, L. |
| title |
Optimal boundary holes for the Sobolev trace constant |
| title_short |
Optimal boundary holes for the Sobolev trace constant |
| title_full |
Optimal boundary holes for the Sobolev trace constant |
| title_fullStr |
Optimal boundary holes for the Sobolev trace constant |
| title_full_unstemmed |
Optimal boundary holes for the Sobolev trace constant |
| title_sort |
optimal boundary holes for the sobolev trace constant |
| publishDate |
2011 |
| url |
http://hdl.handle.net/20.500.12110/paper_00220396_v251_n8_p2327_DelPezzo |
| work_keys_str_mv |
AT delpezzol optimalboundaryholesforthesobolevtraceconstant AT fernandezbonderj optimalboundaryholesforthesobolevtraceconstant AT nevesw optimalboundaryholesforthesobolevtraceconstant |
| _version_ |
1769810273651130368 |