On the stability of the Serrin problem

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An overdetermined problem in Riesz-potential and fractional Laplacian (2011, result): “relies crucially on the linearity of the Laplace operator. Since the work of [Se], many results are obtained about overdetermined problems. The interested reader may refer to [AB], [B], [BK], [BNST], [BNST1], [CS], [EP], [FG], [FGK], [FK], [FV], [G], [GL], [HPP], [Lim], [Liu], [M], [MR], [PP], [PS],”
Overdetermined anisotropic elliptic problems (2009, background): “A partial list of papers on this and related topics includes [1,6, 7 ,13,17,18,25, 26,29].”
Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities (2017, methodology): “ (1.11) and (1.12) and, in Theorems 3.6 and 3.7, we derive two inequalities: (1.14) ρe −ρi ≤ Ckuν −Rk 2/(N+2) 2,Γ and (1.15) ρe −ρi ≤ Ckuν −Rk 1 N+2 1,Γ . The latter clearly improves that obtained in [BNST], while the former makes better than [CMV], even if we replace the Lipschitz semi-norm by an L”
On the Shape of Compact Hypersurfaces with Almost‐Constant Mean Curvature (2015, background): “In our terminology, the main result from [4] states that, ifH0 D n and for some t > 0 one has”