Calculus of Variations and Geometric Measure Theory
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A. Farina - B. Kawohl

Remarks on an overdetermined boundary value problem

created by farina on 26 Apr 2007


Accepted Paper

Inserted: 26 apr 2007

Journal: Calc. Var. Partial Differential Equations
Year: 2007


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


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