Spheres are the unique admissible domains for the exterior overdetermined problem with Neumann data proportional to mean curvature when Γ ≥ N-2 among star-shaped domains (and all bounded domains when Γ = N-2) in N ≥ 3, with further results for Γ ≤ 0 and in 2D.
Symmetry breaking bifurcations for two overdetermined boundary value prob- lems with non-constant Neumann condition on exterior domains inR 3.Comm
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Spherical rigidity for an exterior overdetermined problem with Neumann data prescribed by mean curvature
Spheres are the unique admissible domains for the exterior overdetermined problem with Neumann data proportional to mean curvature when Γ ≥ N-2 among star-shaped domains (and all bounded domains when Γ = N-2) in N ≥ 3, with further results for Γ ≤ 0 and in 2D.