Modica-type estimates and curvature results for overdetermined elliptic problems Ruiz Aguilar, David Sicbaldi, Pieralberto Wu, Jing In this paper, we establish a Modica-type estimate on bounded solutions to the overdetermined elliptic problem. [Δu + f(u) = 0 in Ω , u >0 in Ω , u = 0 on ∂Ω , ∂νu = −κ on ∂Ω] where Ω ⊂ Rn, n ≥ 2. As we will see, the presence of the boundary changes the usual form of the Modica estimate for entire solutions. We will also discuss the equality case. From such estimates, we will deduce information about the curvature of ∂Ω under a certain condition on κ and f. The proof uses the maximum principle together with scaling arguments and a careful passage to the limit in the arguments by contradiction. 2024-10-07T11:37:14Z 2024-10-07T11:37:14Z 2024-09-24 journal article Ruiz Aguilar, D. & Sicbaldi, P. & Wu, J. Communications in Contemporary Mathematics (2024) 2450050. [https://doi.org/10.1142/S0219199724500500] https://hdl.handle.net/10481/95647 10.1142/S0219199724500500 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional World Scientific Publishing