Serrin's overdetermined problem for fully nonlinear nonelliptic equations Gálvez López, José Antonio Mira, Pablo Overdetermined problems Fully nonlinear equations Poincaré-Hopf index Research partially supported by MICINN/FEDER grants no. PID2020-118137GB-I00, CEX2020-001105-M, and Junta de Andalucia grants no. A-FQM-139-UGR18, P18-FR-4049. Let u denote a solution to a rotationally invariant Hessian equation F(D(2)u) = 0 on a bounded simply connected domain Omega subset of R-2, with constant Dirichlet and Neumann data on partial derivative Omega. We prove that if u is real analytic and not identically zero, then u is radial and Omega is a disk. The fully nonlinear operator F not equivalent to 0 is of general type and, in particular, not assumed to be elliptic. We also show that the result is sharp, in the sense that it is not true if Omega is not simply connected, or if u is C-infinity but not real-analytic. 2021-11-12T12:45:53Z 2021-11-12T12:45:53Z 2021-08-22 info:eu-repo/semantics/article Gálvez, J. A., & Mira, P. (2021). Serrin’s overdetermined problem for fully nonlinear nonelliptic equations. Analysis & PDE, 14(5), 1429-1442. [https://doi.org/10.2140/apde.2021.14.1429] http://hdl.handle.net/10481/71474 10.2140/apde.2021.14.1429 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Mathematical Sciences Publishers