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math.AP2021
Backus problem in geophysics: a resolution near the dipole in fractional Sobolev spaces
Toru Kan, Rolando Magnanini, Michiaki Onodera
We consider Backus's problem in geophysics. This consists in reconstructing a harmonic potential outside the Earth when the intensity of the related field is measured on the Earth'…
math.AP2021★ 3 cited
Stability analysis of an overdetermined fourth order boundary value problem via an integral identity
Yuya Okamoto, Michiaki Onodera
We consider an overdetermined fourth order boundary value problem in which the boundary value of the Laplacian of the solution is prescribed, in addition to the homogeneous Dirichl…
math.AP2021★ 2 cited
Linear stability estimates for Serrin's problem via a modified implicit function theorem
Alexandra Gilsbach, Michiaki Onodera
We examine Serrin's classical overdetermined problem under a perturbation of the Neumann boundary condition. The solution of the problem for a constant Neumann boundary condition e…