Artículo
Pinasco, J.P.; Rossi, J.D. "Asymptotics of the spectral function for the Steklov problem in a family of sets with fractal boundaries" (2005) Applied Mathematics E - Notes. 5:138-146
Estamos trabajando para incorporar este artículo al repositorio
Consulte la política de Acceso Abierto del editor
Abstract:
In this paper we find the asymptotic behavior of the spectral counting function for the Steklov problem in a family of self similar domains with fractal boundaries. Using renewal theory, we show that the main term in the asymptotics depends on the Minkowski dimension of the boundary. Also, we compute explicitly a three term expansion for a family of self similar sets, and a two term asymptotic expansion for a family of non self similar sets.
Registro:
| Documento: | Artículo |
| Título: | Asymptotics of the spectral function for the Steklov problem in a family of sets with fractal boundaries |
| Autor: | Pinasco, J.P.; Rossi, J.D. |
| Filiación: | Departamento de Matemática, FCEyN, UBA, (1428) Buenos Aires, Argentina |
| Año: | 2005 |
| Volumen: | 5 |
| Página de inicio: | 138 |
| Página de fin: | 146 |
| Título revista: | Applied Mathematics E - Notes |
| Título revista abreviado: | Appl. Math. E - Notes |
| ISSN: | 16072510 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16072510_v5_n_p138_Pinasco |
Referencias:
- Van Der Berg, M., Levitin, M., Functions of Weierstrass type and spectral asymptotics for iterated sets (1996) Quart. J. Math. Oxford Ser. (2), 47, pp. 493-509
- Besicovitch, Taylor, J., On the complementary intervals of a linear closed set of zero Lebesgue measure (1954) J. London Math. Soc., 29, pp. 449-459
- Falconer, K., (1990) Fractal Geometry, , Math. Foundations and Appl. J. Wiley & Sons
- Fleckinger, J., Vassiliev, D., An example of a two-term asymptotics for the "Counting Function" of a fractal drum (1993) Trans. A. M. S., 337 (1), pp. 99-116
- Kac, M., Can one hear the shape of a drum? (1966) Amer. Math. Monthly (Slaught Mem. Papers, No. 11), 73 (4), pp. 1-23
- Kratzel, E., (1988) Lattice Points, , Kluwer Academic Publishers
- Lapidus, M., Fractal drum, inverse spectral problems for elliptic operators and a partial resolution of the Weyl-Berry conjecture (1991) Trans. A. M. S., 325 (2), pp. 465-528
- Lapidus, M., Pomerance, C., The Riemann zeta-function and the one-dimensional Weyl-Berry conjecture for fractal drums (1993) Proc. London Math. Soc., 66 (3), pp. 41-69
- Levitin, M., Vassiliev, D., Spectral asymptotics, renewal theorem and the Berry conjecture for a class of fractals (1996) Proc. London Math. Soc., 72 (3), pp. 188-214
- Martio, O., Vuorinen, M., Whitney cubes, p-capacity, and Minkowski content (1987) Expo. Math., 5, pp. 17-40
- Mattila, P., Geometry of sets and measures in Euclidean spaces (1995) Cambridge Studies in Adv. Math., 44. , Cambridge Univ. Press
- Pinasco, J.P., (2002) Asymptotic of Eigenvalues of the p-Laplace Operator and Lattice Points, , Preprint, Universidad de Buenos Aires
- Sandgren, L., A vibration problem (1955) Medd. Lund Univ. Mat. Sem., 13, pp. 1-84
Citas:
---------- APA ----------
Pinasco, J.P. & Rossi, J.D. (2005) . Asymptotics of the spectral function for the Steklov problem in a family of sets with fractal boundaries. Applied Mathematics E - Notes, 5, 138-146.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16072510_v5_n_p138_Pinasco [ ]
---------- CHICAGO ----------
Pinasco, J.P., Rossi, J.D. "Asymptotics of the spectral function for the Steklov problem in a family of sets with fractal boundaries" . Applied Mathematics E - Notes 5 (2005) : 138-146.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16072510_v5_n_p138_Pinasco [ ]
---------- MLA ----------
Pinasco, J.P., Rossi, J.D. "Asymptotics of the spectral function for the Steklov problem in a family of sets with fractal boundaries" . Applied Mathematics E - Notes, vol. 5, 2005, pp. 138-146.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16072510_v5_n_p138_Pinasco [ ]
---------- VANCOUVER ----------
Pinasco, J.P., Rossi, J.D. Asymptotics of the spectral function for the Steklov problem in a family of sets with fractal boundaries. Appl. Math. E - Notes. 2005;5:138-146.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16072510_v5_n_p138_Pinasco [ ]
