Vol. 14, No. 5, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 6, 1671–1976
Issue 5, 1333–1669
Issue 4, 985–1332
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Serrin's overdetermined problem for fully nonlinear nonelliptic equations

José A. Gálvez and Pablo Mira

Vol. 14 (2021), No. 5, 1429–1442
Abstract

Let u denote a solution to a rotationally invariant Hessian equation F(D2u) = 0 on a bounded simply connected domain Ω 2, with constant Dirichlet and Neumann data on Ω. We prove that if u is real analytic and not identically zero, then u is radial and Ω is a disk. The fully nonlinear operator F0 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 Ω is not simply connected, or if u is C but not real-analytic.

Keywords
overdetermined problems, fully nonlinear equations, Poincaré–Hopf index
Mathematical Subject Classification 2010
Primary: 35N25, 35M12, 53A10
Milestones
Received: 5 February 2019
Accepted: 27 January 2020
Published: 22 August 2021
Authors
José A. Gálvez
Departamento de Geometría y Topología
Universidad de Granada
Granada
Spain
Pablo Mira
Departamento de Matemática Aplicada y Estadística
Universidad Politécnica de Cartagena
Cartagena
Spain