Serrin's overdetermined problem for fully nonlinear nonelliptic equations
Metadatos
Mostrar el registro completo del ítemEditorial
Mathematical Sciences Publishers
Materia
Overdetermined problems Fully nonlinear equations Poincaré-Hopf index
Fecha
2021-08-22Referencia bibliográfica
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]
Patrocinador
Spanish Government European Commission PID2020-118137GB-I00 CEX2020-001105-M; Junta de Andalucia A-FQM-139-UGR18 P18-FR-4049Resumen
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.