An optimization problem related to the best Sobolev trace constant in thin domains

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Let Ω ⊂ ℝN be a bounded, smooth domain. We deal with the best constant of the Sobolev trace embedding W1,p(Ω) Rightwards arrow with hook sign Lq (∂Ω) for functions that vanish in a subset A ⊂ Ω, which we call the hole, i.e. we deal with the minimization problem SA = inf||u||W 1,p(ω)p/||u||Lq(∂ω) for...

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Detalles Bibliográficos
Autor principal: Bonder, J.F
Otros Autores: Rossi, J.D, SchÖnlieb, C.-B
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2008
Acceso en línea:Registro en Scopus
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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024 7 |2 scopus  |a 2-s2.0-51449089699 
040 |a Scopus  |b spa  |c AR-BaUEN  |d AR-BaUEN 
100 1 |a Bonder, J.F. 
245 1 3 |a An optimization problem related to the best Sobolev trace constant in thin domains 
260 |c 2008 
270 1 0 |m Bonder, J. F.; Departamento de Matemática, FCEyN UBA (1428), Buenos Aires, Argentina; email: jfbonder@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Aubin, T., Équations différentielles non linéaires et le problème de Yamabe concernant la courbure scalaire (1976) J. Math. Pures Appl, 55, pp. 269-296 
504 |a Biezuner, R.J., Best constants in Sobolev trace inequalities (2003) Nonlinear Anal, 54, pp. 575-589 
504 |a Binding, P., Boulton, L., Cepicka, J., Drabek, P., Girg, P., Basic properties of eigen-functions of the p-Laplacian (2006) Proc. Amer. Math. Soc, 134 (12), pp. 3487-3494 
504 |a Cherkaev, A., Cherkaeva, E., Optimal design for uncertain loading condition (1999) Ser. Adv. Math. Appl. Sci, 50, pp. 193-213. , Homogenization, World Sci. Publishing, River Edge, NJ 
504 |a Druet, O., Hebey, E., The AB program in geometric analysis: Sharp Sobolev inequalities and related problems (2002) Mem. Amer. Math. Soc, 160 (761). , viii, 98pp 
504 |a del Pino, M., Flores, C., Asymptotic behavior of best constants and extremals for trace embeddings in expanding domains (2001) Comm. Partial Differential Equations, 26 (11-12), pp. 2189-2210 
504 |a Escobar, J.F., Sharp constant in a Sobolev trace inequality (1988) Indiana Math. J, 37 (3), pp. 687-698 
504 |a Fernández Bonder, J., Lami Dozo, E., Rossi, J.D., Symmetry properties for the extremals of the Sobolev trace embedding (2004) Ann. Inst. H. Poincaré Anal. Non Linéaire, 21 (6), pp. 795-805 
504 |a Fernandez Bonder, J., Ferreira, R., Rossi, J.D., Uniform bounds for the best Sobolev trace constant (2003) Adv. Nonlinear Stud, 3 (2), pp. 181-192 
504 |a Fernández Bonder, J., Groisman, P., Rossi, J.D., Optimization of the first Steklov eigenvalue in domains with holes: A shape derivative approach (2007) Ann. Mat. Pura Appl, 186 (2), pp. 341-358 
504 |a Fernandez Bonder, J., Martinez, S., Rossi, J.D., The behavior of the best Sobolev trace constant and extremals in thin domains (2004) J. Differential Equations, 198 (1), pp. 129-148 
504 |a Fernández Bonder, J., Rossi, J.D., Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains (2002) Comm. Pure Appl. Anal, 1 (3), pp. 359-378 
504 |a Fernández Bonder, J., Rossi, J.D., Wolanski, N., Behavior of the best Sobolev trace constant and extremals in domains with holes (2006) Bull. Sci. Math, 130, pp. 565-579 
504 |a Fernández Bonder, J., Rossi, J.D., Wolanski, N., Regularity of the free boundary in an optimization problem related to the best Sobolev trace constant (2005) SIAM J. Control Optim, 44 (5), pp. 1614-1635 
504 |a Henrot, A., Minimization problems for eigenvalues of the Laplacian (2003) J. Evol. Equ, 3 (3), pp. 443-461 
504 |a Lami Dozo, E., Torne, O., Symmetry and symmetry breaking for minimizers in the trace inequality (2005) Commun. Contemp. Math, 7 (6), pp. 727-756 
504 |a Li, Y., Zhu, M., Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries (1997) Comm. Pure Appl. Math, 50, pp. 449-487 
504 |a Martinez, S., Rossi, J.D., Isolation and simplicity for the first eigenvalue of the p-Laplacian with a nonlinear boundary condition (2002) Abstr. Appl. Anal, 7 (5), pp. 287-293 
520 3 |a Let Ω ⊂ ℝN be a bounded, smooth domain. We deal with the best constant of the Sobolev trace embedding W1,p(Ω) Rightwards arrow with hook sign Lq (∂Ω) for functions that vanish in a subset A ⊂ Ω, which we call the hole, i.e. we deal with the minimization problem SA = inf||u||W 1,p(ω)p/||u||Lq(∂ω) for functions that verify u|A = 0. It is known that there exists an optimal hole that minimizes the best constant SA among subsets of Ω of the prescribed volume. In this paper, we look for optimal holes and extremals in thin domains. We find a limit problem (when the thickness of the domain goes to zero), that is a standard Neumann eigenvalue problem with weights and prove that when the domain is contracted to a segment, it is better to concentrate the hole on one side of the domain. © 2008 World Scientific Publishing Company.  |l eng 
536 |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, PICT2006 – 290 
536 |a Detalles de la financiación: Universidad de Buenos Aires, X078 
536 |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PIP 5478/1438 
536 |a Detalles de la financiación: Austrian Science Fund 
536 |a Detalles de la financiación: Austrian Science Fund 
536 |a Detalles de la financiación: Vienna Science and Technology Fund, CI06 003 
536 |a Detalles de la financiación: Canadian Blood Services 
536 |a Detalles de la financiación: JFB was partially supported by Universidad de Buenos Aires under grant X078, by Agencia Nacional de Promoción Científica y Tecnológica under grant PICT2006 – 290 and by CONICET under grant PIP 5478/1438. 
536 |a Detalles de la financiación: CBS was partially supported by the WWTF (Wiener Wissenschafts-, Forschungs-und Technologiefonds) project nr. CI06 003, the PhD program (Wissenschaftskolleg) taking place at the University of Vienna, the FWF (Fonds zur Förderung der wissenschaftlichen Forschung) Wittgenstein award of Peter Markowich, project nr. Z-50 MAT and the FFG (Österreichische Forschungsförderungsgesellschaft), project number 813610. 
593 |a Departamento de Matemática, FCEyN UBA (1428), Buenos Aires, Argentina 
593 |a IMDEA Matematicas, C-IX Campus UAM, Madrid, Spain 
593 |a DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom 
593 |a Faculty of Mathematics, University of Vienna, Nordbergstr. 15, 1090, Vienna, Austria 
690 1 0 |a CALCULUS OF VARIATIONS 
690 1 0 |a OPTIMAL DESIGN 
690 1 0 |a SOBOLEV TRACE EMBEDDING 
700 1 |a Rossi, J.D. 
700 1 |a SchÖnlieb, C.-B. 
773 0 |d 2008  |g v. 10  |h pp. 633-650  |k n. 5  |p Commun. Contemp. Math.  |x 02191997  |w (AR-BaUEN)CENRE-4244  |t Communications in Contemporary Mathematics 
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856 4 0 |u https://doi.org/10.1142/S0219199708002922  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_02191997_v10_n5_p633_Bonder  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v10_n5_p633_Bonder  |y Registro en la Biblioteca Digital 
961 |a paper_02191997_v10_n5_p633_Bonder  |b paper  |c PE 
962 |a info:eu-repo/semantics/article  |a info:ar-repo/semantics/artículo  |b info:eu-repo/semantics/publishedVersion 
999 |c 66617 

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