Regularity of the free boundary in an optimization problem related to the best sobolev trace constant

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In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion H1(Ω) → Lq(∂Ω) for functions that vanish in a subset of Ω. This problem is also related to a minimization problem for Steklov eigenvalues. © 200...

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Autor principal: Bonder, J.F
Otros Autores: Rossi, J.D, Wolanski, N.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2006
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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100 1 |a Bonder, J.F. 
245 1 0 |a Regularity of the free boundary in an optimization problem related to the best sobolev trace constant 
260 |c 2006 
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 Adams, R.A., Sobolev spaces (1975) Pure and Applied Mathematics, 65. , Academic Press, New York, London 
504 |a Aguilera, N., Alt, H.W., Caffarelli, L.A., An optimization problem with volume constraint (1986) SIAM J. Control Optim., 24, pp. 191-198 
504 |a Aguilera, N., Caffarelli, L.A., Spruck, J., An optimization problem in heat conduction (1988) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 14, pp. 355-387 
504 |a Alt, H.W., Caffarelli, L.A., Existence and regularity for a minimum problem with free boundary, 3 (1981) Reine Angew. Math., 325, pp. 105-144 
504 |a Alt, H.W., Caffarelli, L.A., Friedman, A., A free boundary problem for quasilinear elliptic equations (1984) Ann. Scuola Norm. Sup. Pisa Cl., Sci. (4), 11, pp. 1-44 
504 |a Aubin, T., Equations différentielles non linéaires et le problème de Yamabe concernant la courbure scalaire (1976) J. Math. Pures Appl. (9), 55, pp. 269-296 
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) 
504 |a Federer, H., Geometric measure theory (1969) Grundlehren Math. Wiss., 153. , Springer-Verlag, New York 
504 |a Bonder, J.F., Rossi, J.D., Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains (2002) Commun. Pure Appl. Anal., 1, pp. 359-378 
504 |a Bonder, J.F., Rossi, J.D., Wolanski, N., (2004) On the Best Sobolev Trace Constant and Extremals in Domains with Holes, , preprint, University of Buenos Aires, Buenos Aires 
504 |a Flores, C., Del Pino, M., Asymptotic behavior of best constants and extremals for trace embeddings in expanding domains (2001) Comm. Partial Differential Equations, 26, pp. 2189-2210 
504 |a Gilbarg, D., Trudinger, N.S., Elliptic partial differential equations of second order (1983) Grundlehren Math. Wiss., 224. , Springer-Verlag, Berlin 
504 |a Henrot, A., Minimization problems for eigenvalues of the Laplacian, 3 (2003) Evol. Equ., 3, pp. 443-461 
504 |a Kawohl, B., Rearrangements and convexity of level sets in PDE (1985) Lecture Notes in Math., 1150. , Springer-Verlag, Berlin 
504 |a Lederman, C., An optimization problem in elasticity (1995) Differential Integral Equations, 8, pp. 2025-2044 
504 |a Lederman, C., A free boundary problem with a volume penalization (1996) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 23, pp. 249-300 
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 Lieb, E.H., Loss, M., Analysis (2001) Grad. Stud. Math. 14, 2nd Ed., 14. , AMS, Providence, RI 
504 |a Steklov, M.W., Sur les problèmes fondamentaux en physique mathématique (1902) Ann. Sci. École Norm. Sup. (4), 19, pp. 455-490 
504 |a Teixeira, E., A nonlinear optimization problem in heat conduction (2005) Calc. Var. Partial Differential Equations, 24, pp. 21-46 
520 3 |a In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion H1(Ω) → Lq(∂Ω) for functions that vanish in a subset of Ω. This problem is also related to a minimization problem for Steklov eigenvalues. © 2005 Society for Industrial and Applied Mathematics.  |l eng 
593 |a Departamento de Matemática, FCEyN, UBA, (1428) Buenos Aires, Argentina 
593 |a Consejo Superior de Investigaciones Científicas (CSIC), Serrano 117, Madrid, Spain 
690 1 0 |a EIGENVALUE OPTIMIZATION PROBLEMS 
690 1 0 |a FREE BOUNDARIES 
690 1 0 |a SOBOLEV TRACE CONSTANT 
690 1 0 |a EIGENVALUES AND EIGENFUNCTIONS 
690 1 0 |a MATHEMATICAL MODELS 
690 1 0 |a OPTIMIZATION 
690 1 0 |a PROBLEM SOLVING 
690 1 0 |a THEOREM PROVING 
690 1 0 |a EIGENVALUE OPTIMIZATION PROBLEMS 
690 1 0 |a FREE BOUNDARIES 
690 1 0 |a SOBOLEV TRACE CONSTANT 
690 1 0 |a BOUNDARY VALUE PROBLEMS 
700 1 |a Rossi, J.D. 
700 1 |a Wolanski, N. 
773 0 |d 2006  |g v. 44  |h pp. 1614-1635  |k n. 5  |p SIAM J Control Optim  |x 03630129  |w (AR-BaUEN)CENRE-255  |t SIAM Journal on Control and Optimization 
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856 4 0 |u https://doi.org/10.1137/040613615  |y DOI 
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