Uniform stability of the ball with respect to the first Dirichlet and Neumann infinity-eigenvalues
| dc.contributor.author | da Silva, Joao Vitor | |
| dc.contributor.author | Rossi, Julio D. | |
| dc.contributor.author | Salort, Ariel M. | |
| dc.date.accessioned | 2021-12-17T16:54:48Z | |
| dc.date.available | 2021-12-17T16:54:48Z | |
| dc.date.issued | 2018-01-06 | |
| dc.description.abstract | In this note we analyze how perturbations of a ball Br ⊂ ℝn behaves in terms of their first (non-trivial) Neumann and Dirichlet ∞-eigenvalues when a volume constraint ℒn(Ω) = ℒn(Br) is imposed. Our main result states that Ω is uniformly close to a ball when it has first Neumann and Dirichlet eigenvalues close to the ones for the ball of the same volume Br. In fact, we show that, if |λD1,∞(Ω) - λD1,∞ (Br)| = δ1 and |λN1,∞(Ω) - λN1,∞(Br)| = δ2, then there are two balls such that B r\δ1r+1 ⊂ Ω ⊂ B r+δ2r∙/1-δ2r In addition, we obtain a result concerning stability of the Dirichlet ∞-eigenfunctions. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 9 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | da Silva, J. V., Rossi, J. D., & Salort, A. M. (2018). Uniform stability of the ball with respect to the first Dirichlet and Neumann infinity-eigenvalues. <i>Electronic Journal of Differential Equations, 2018</i>(07), pp. 1-9. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15062 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Infinity-eigenvalues estimates | |
| dc.subject | Infinity-eigenvalue problem | |
| dc.subject | Approximation of domains | |
| dc.title | Uniform stability of the ball with respect to the first Dirichlet and Neumann infinity-eigenvalues | |
| dc.type | Article |