Inserted: 26 apr 2007
Journal: Calc. Var. Partial Differential Equations
We modify and extend proofs of Serrin's symmetry result for overdetermined boundary value problems from the Laplace-operator to a general quasilinear operator and remove a strong ellipticity assumption in 9 and a growth assumption in 5 on the diffusion coefficient $A$, as well as a starshapedness assumption on the set $ \Omega $ in 4.
Keywords: symmetry, overdetermined boundary problem, isoparametric surfaces, Pohozaev identity