da Silva, Joao VitorRossi, Julio D.Salort, Ariel M.2021-12-172021-12-172018-01-06da 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. 1-9.1072-6691https://hdl.handle.net/10877/15062In 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.Text9 pages1 file (.pdf)enAttribution 4.0 InternationalInfinity-eigenvalues estimatesInfinity-eigenvalue problemApproximation of domainsArticle