Artículo
Canuto, B.; Rial, D. "Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign" (2008) Rendiconti dell'Istituto di Matematica dell'Universita di Trieste. 40:1-27
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Abstract:
We prove that the only domain Ω such that there exists a solution to the following overdetermined problem Δu+ω2u=-1 in Ω, u=0 on ∂Ω, and ∂nu=c on ∂Ω, is the ball B1, independently on the sign of u, if we assume that the boundary ∂Ω is a perturbation (no necessarily regular) of the unit sphere ∂B1 of ℝn. Here ω2 ≠ (λn)n≥1 (the eigenvalues of -Δ in B1 with Dirichlet boundary conditions), and ω ∉ Λ, where Λ is a enumerable set of ℝ+, whose limit points are the values λ1m, for some integer m ≤ 1, λ1m being the mth-zero of the first-order Bessel function I1. © 2009, EUT Edizioni Universita di Trieste.
Registro:
| Documento: | Artículo |
| Título: | Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign |
| Autor: | Canuto, B.; Rial, D. |
| Filiación: | Dpto. de Matemática, FCEyN, Univ. de Buenos Aires, Buenos Aires, Argentina |
| Palabras clave: | Elliptic equation; Overdetermined boundary value problem; Radial symmetry |
| Año: | 2008 |
| Volumen: | 40 |
| Página de inicio: | 1 |
| Página de fin: | 27 |
| Título revista: | Rendiconti dell'Istituto di Matematica dell'Universita di Trieste |
| Título revista abreviado: | Rendicont. dell'Istituto Matemat. dell'Universita Trieste |
| ISSN: | 00494704 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00494704_v40_n_p1_Canuto |
Referencias:
- Choulli, M., Henrot, A., Use of the domain derivative to prove symmetry results in partial differential equations (1998) Math. Nachr, 192, pp. 91-103
- Courant, R., Hilbert, D., (1953) Methods of mathematical physics, 1. , Interscience Publishers, U.S.A
- Flajolet, P., Schott, R., Non-overlapping partitions, contin-ued fractions Bessel functions and a divergent series (1990) European Jour. Combin, 11, pp. 412-432
- Gilbarg, D., Trudinger, N.S., (1983) Elliptic partial differential equa-tions of second order, , Springer, U.S.A
- Maki, D., On constructing of distribution functions with applications to Lommel polynomials and Bessel functions (1968) Trans. Amer. Math. Soc, 130, pp. 281-297
- Serrin, J., A symmetry problem in potential theory (1971) Arch. Rat. Mech. Anal, 43, pp. 304-318
Citas:
---------- APA ----------
Canuto, B. & Rial, D. (2008) . Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign. Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, 40, 1-27.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00494704_v40_n_p1_Canuto [ ]
---------- CHICAGO ----------
Canuto, B., Rial, D. "Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign" . Rendiconti dell'Istituto di Matematica dell'Universita di Trieste 40 (2008) : 1-27.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00494704_v40_n_p1_Canuto [ ]
---------- MLA ----------
Canuto, B., Rial, D. "Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign" . Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, vol. 40, 2008, pp. 1-27.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00494704_v40_n_p1_Canuto [ ]
---------- VANCOUVER ----------
Canuto, B., Rial, D. Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign. Rendicont. dell'Istituto Matemat. dell'Universita Trieste. 2008;40:1-27.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00494704_v40_n_p1_Canuto [ ]
