Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian
| Parent link: | Journal of Mathematical Analysis and Applications Vol. 463, iss. 1.— 2018.— [P. 19-39] |
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| Autor principal: | |
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| Otros Autores: | , |
| Sumario: | Title screen In this paper we study integral estimates of derivatives of conformal mappings φ:D→Ω of the unit disc D⊂C onto bounded domains Ω that satisfy the Ahlfors condition. These integral estimates lead to estimates of constants in Sobolev-Poincaré inequalities, and by the Rayleigh quotient we obtain spectral estimates of the Neumann-Laplace operator in non-Lipschitz domains (quasidiscs) in terms of the (quasi)conformal geometry of the domains. Specifically, the lower estimates of the first non-trivial eigenvalues of the Neumann-Laplace operator in some fractal type domains (snowflakes) were obtained. Режим доступа: по договору с организацией-держателем ресурса |
| Lenguaje: | inglés |
| Publicado: |
2018
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| Materias: | |
| Acceso en línea: | https://doi.org/10.1016/j.jmaa.2018.02.063 |
| Formato: | Electrónico Capítulo de libro |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=658512 |