Stability of a class of a Serrin's problem with multiple perturbations
In this paper,we investigate the stability of a Serrin-type overdetermined problem with perturbations in the unknown subdomain and boundary conditions.A quantitative stability estimate is established by measuring the deviation between the domain and a sphere.We prove that when the subdomain has a small Lebesgue measure and the outward normal derivative on the boundary approaches a constant,the domain is geometrically close to a sphere.The proof is based on a Rellich-Pohozaev-type integral identity.
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