@misc{10481/95647,
year = {2024},
month = {9},
url = {https://hdl.handle.net/10481/95647},
abstract = {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.},
organization = {D.R. has been supported by the FEDER-MINECO Grant PID2021-122122NBI00
and by J. Andalucia (FQM-116)},
organization = {P.S. has been supported by the FEDERMINECO
Grants PID2020-117868GB-I00 and PID2023-150727NB-I00 and by J.
Andalucia Grant P18-FR-4049},
organization = {J.W. has been supported by the China Scholarship
Council (CSC201906290013) and by J. Andalucia (FQM-116)},
organization = {D.R. and P.S. also
acknowledge financial support from the Spanish Ministry of Science and Innovation
(MICINN), through the IMAG-Maria de Maeztu Excellence Grant CEX2020-
001105-M/AEI/10.13039/501100011033},
publisher = {World Scientific Publishing},
title = {Modica-type estimates and curvature results for overdetermined elliptic problems},
doi = {10.1142/S0219199724500500},
author = {Ruiz Aguilar, David and Sicbaldi, Pieralberto and Wu, Jing},
}