Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems
In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality λ1(Ω) ∥u∥L1(∂Ω) ≤ ∥u∥ W1,1(Ω) that are independent of Ω. These estimates generalize those of [J. Fernandez Bonder, N. Saintier, Estimates for the Sobolev trace constant with critical exponent and applic...
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Elsevier Ltd
2008
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| 005 | 20230518203518.0 | ||
| 008 | 190411s2008 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-79955594365 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a NOAND | ||
| 100 | 1 | |a Saintier, N. | |
| 245 | 1 | 0 | |a Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems |
| 260 | |b Elsevier Ltd |c 2008 | ||
| 270 | 1 | 0 | |m Saintier, N.; Departamento de Matemática, FCEyN UBA, (1428), Buenos Aires, Argentina; email: nsaintie@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Evans, L.C., Gariepy, R.F., Measure theory and fine properties of functions (1992) Studies in Advanced Math., , CRC Press, Ann Harbor | ||
| 504 | |a Fernandez Bonder, J., Saintier, N., Estimates for the Sobolev trace constant with critical exponent and applications Ann. Mat. Pura. Aplicata, , in press | ||
| 504 | |a Fernández Bonder, J., Rossi, J.D., Wolanski, N., On 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 (2006) SIAM J. Control Optim., 44 (5), pp. 1614-1635 | ||
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| 504 | |a (1968) Sibirskii Mathematicheskii Zhurnal, 9, pp. 1386-1394. , Translated from | ||
| 504 | |a Saintier, N., Shape Derivative of the First Eigenvalue of the 1-Laplacian, , submitted for publication | ||
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| 520 | 3 | |a In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality λ1(Ω) ∥u∥L1(∂Ω) ≤ ∥u∥ W1,1(Ω) that are independent of Ω. These estimates generalize those of [J. Fernandez Bonder, N. Saintier, Estimates for the Sobolev trace constant with critical exponent and applications, Ann. Mat. Pura. Aplicata (in press)] concerning the p-Laplacian to the case p = 1. We apply our results to prove the existence of an extremal for this embedding.We then study an optimal design problem related to λ1, and eventually compute the shape derivative of the functional Ω → λ1(Ω) © 2007 Elsevier Ltd. All rights reserved. |l eng | |
| 536 | |a Detalles de la financiación: Fondo para la Investigación Científica y Tecnológica, PICT 03-13719 | ||
| 536 | |a Detalles de la financiación: The author acknowledges the support of the grant FONCYT PICT 03-13719 (Argentina) and would like to express his gratitude to Prof. J.D. Rossi for help. | ||
| 593 | |a Departamento de Matemática, FCEyN UBA, (1428), Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a 1-LAPLACIAN |
| 690 | 1 | 0 | |a CRITICAL EXPONENTS |
| 690 | 1 | 0 | |a FUNCTIONS OF BOUNDED VARIATIONS |
| 690 | 1 | 0 | |a OPTIMAL DESIGN PROBLEMS |
| 690 | 1 | 0 | |a SHAPE ANALYSIS |
| 690 | 1 | 0 | |a SOBOLEV TRACE EMBEDDING |
| 690 | 1 | 0 | |a OPTIMAL SYSTEMS |
| 690 | 1 | 0 | |a OPTIMIZATION |
| 690 | 1 | 0 | |a 1-LAPLACIAN |
| 690 | 1 | 0 | |a CRITICAL EXPONENT |
| 690 | 1 | 0 | |a FUNCTIONS OF BOUNDED VARIATIONS |
| 690 | 1 | 0 | |a OPTIMAL DESIGN |
| 690 | 1 | 0 | |a SHAPE ANALYSIS |
| 690 | 1 | 0 | |a SOBOLEV |
| 690 | 1 | 0 | |a SHAPE OPTIMIZATION |
| 773 | 0 | |d Elsevier Ltd, 2008 |g v. 69 |h pp. 2479-2491 |k n. 8 |p Nonlinear Anal Theory Methods Appl |x 0362546X |w (AR-BaUEN)CENRE-254 |t Nonlinear Analysis, Theory, Methods and Applications | |
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| 856 | 4 | 0 | |u https://doi.org/10.1016/j.na.2007.08.026 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_0362546X_v69_n8_p2479_Saintier |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v69_n8_p2479_Saintier |y Registro en la Biblioteca Digital |
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