Estimates for the Sobolev trace constant with critical exponent and applications
In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality S∥u∥Lp*(∂Ω) p≤∥u∥W1,p(Ω) that are independent of Ω. This estimates generalized those of Adimurthi and Yadava (Comm Partial Diff Equ 16(11):1733-1760, 1991) for general p. Here p*: = p(N - 1)/(N - p) is...
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2008
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| 008 | 190411s2008 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-45749138041 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Fernández Bonder, J. | |
| 245 | 1 | 0 | |a Estimates for the Sobolev trace constant with critical exponent and applications |
| 260 | |c 2008 | ||
| 270 | 1 | 0 | |m Fernández Bonder, J.; Departamento de Matemática, FCEyN UBA, (1428), Buenos Aires, Argentina; email: jfbonder@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Aubin, T., Equations différentielles non-linéaires et le problème de Yamabé concernant la courbure scalaire (1976) J. Math. Pures Appl., 55, pp. 269-296 | ||
| 504 | |a Adimurthi, S.L., Yadava: Positive solution for Neumann problem with critical non-linearity on boundary (1991) Commun. Partial Diff. Equ., 16, pp. 1733-1760. , 11 | ||
| 504 | |a Biezuner, R.J., Best constants in Sobolev trace inequalities (2003) Nonlinear Anal., 54, pp. 575-589. , 3 | ||
| 504 | |a Cherrier, P., Problèmes de Neumann non-linéaires sur les variétés Riemanniennes (1984) J. Funct. Anal., 57, pp. 154-206 | ||
| 504 | |a Cherkaev, A., Cherkaeva, E., Optimal Design for Uncertain Loading Condition, Homogenization (1999) Ser. Adv. Math. Appl. Sci., 50. , World Sci. Publishing, River Edge, NJ 193-213 | ||
| 504 | |a Demengel, F., Nazaret, B., On some nonlinear partial differential equations involving the p-laplacian and critical Sobolev trace maps (2000) Asymptot. Anal., 23, pp. 135-156. , 2 | ||
| 504 | |a Del Pino, M., Flores, C., Asymptotic behavior of best constants and extremals for trace embeddings in expanding domains (2001) Commun. Partial Diff. Equ., 26, pp. 2189-2210. , 11-12 | ||
| 504 | |a Druet, O., Hebey, E., The AB program in geometric analysis: Sharp Sobolev inequalities and related problems (2002) Mem. Am. Math. Soc., 160 | ||
| 504 | |a Escobar, J.F., Sharp constant in a Sobolev trace inequality (1988) Indiana Univ. Math. J., 37, pp. 687-698 | ||
| 504 | |a Fernández Bonder, J., Groisman, P., Rossi, J.D., Optimization of the first Steklov eigenvalue in domains with holes: A shape derivative approach Ann. Mat. Pura Appl., , (to appear) | ||
| 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, pp. 795-805. , 6 | ||
| 504 | |a Fernández Bonder, J., Ferreira, R., Rossi, J.D., Uniform bounds for the best Sobolev trace constant (2003) Adv. Nonlinear Stud., 3, pp. 181-192. , 2 | ||
| 504 | |a Fernández Bonder, J., Rossi, J.D., Existence results for the p-Laplacian with nonlinear boundary conditions (2001) J. Math. Anal. Appl., 263, pp. 195-223 | ||
| 504 | |a Fernández Bonder, J., Rossi, J.D., On the existence of extremals for the Sobolev trace embedding theorem with critical exponent (2005) Bull. Lond. Math. Soc., 37, pp. 119-125 | ||
| 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, pp. 1614-1635. , 5 | ||
| 504 | |a Li, Y., Zhu, M., Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries (1997) Commun. Pure Appl. Math., 50, pp. 449-487 | ||
| 504 | |a Lions, P.L., The concentration-compactness principle in the calculus of variations - The limit case part. 2 (1985) Rev Mat. Iberoam., 1, pp. 45-121. , 2 | ||
| 504 | |a Nazaret, B., Best constants in Sobolev trace inequalities on the half-space Nonlinear Analysis, , (to appear) | ||
| 504 | |a Saintier, N., Asymptotic estimates and blow-up theory for critical equations involving the p-Laplacian (2006) Calc. Var. Partial Diff. Equ., 25, pp. 299-311. , 3 | ||
| 504 | |a Willem, M., Minimax theorem (1996) Progress in Nonlinear Differential Equations and Their Applications, , Birkhäuser | ||
| 520 | 3 | |a In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality S∥u∥Lp*(∂Ω) p≤∥u∥W1,p(Ω) that are independent of Ω. This estimates generalized those of Adimurthi and Yadava (Comm Partial Diff Equ 16(11):1733-1760, 1991) for general p. Here p*: = p(N - 1)/(N - p) is the critical exponent for the immersion and N is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of Fernández Bonder and Rossi (Bull Lond Math Soc 37:119-125, 2005). Finally, we study an optimal design problem with critical exponent. © 2007 Springer-Verlag. |l eng | |
| 593 | |a Departamento de Matemática, FCEyN UBA, (1428), Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a CRITICAL EXPONENTS |
| 690 | 1 | 0 | |a OPTIMAL DESIGN PROBLEMS |
| 690 | 1 | 0 | |a SOBOLEV TRACE EMBEDDING |
| 700 | 1 | |a Saintier, N. | |
| 773 | 0 | |d 2008 |g v. 187 |h pp. 683-704 |k n. 4 |p Ann. Mat. Pura Appl. |x 03733114 |w (AR-BaUEN)CENRE-1530 |t Annali di Matematica Pura ed Applicata | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-007-0062-1 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_03733114_v187_n4_p683_FernandezBonder |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v187_n4_p683_FernandezBonder |y Registro en la Biblioteca Digital |
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| 999 | |c 66627 | ||