Reconstruction of singularities of a scattering potential in two dimensions

DOI10.1006/AAMA.1994.1003zbMath0810.35149OpenAlexW2022841576MaRDI QIDQ1325758

Lassi Päivärinta, Erkki Somersalo, Valery Serov

Publication date: 24 April 1995

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aama.1994.1003

zbMATH Keywords

potential scatteringscattering amplitudeBorn approximationpotential theory in Besov spaces

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (11)

Reconstruction of singularities from full scattering data by new estimates of bilinear Fourier multipliers ⋮ Partial recovery of potentials in generalized nonlinear Schrödinger equations on the line ⋮ Recovery of the singularities of a potential from backscattering data in general dimension ⋮ RECOVERING SINGULARITIES FROM BACKSCATTERING IN TWO DIMENSIONS ⋮ Numerical approximation of the potential in the two-dimesional inverse scattering problem ⋮ INVERSE BORN APPROXIMATION FOR THE GENERALIZED NONLINEAR SCHRÖDINGER OPERATOR IN TWO DIMENSIONS ⋮ The double dispersion operator in backscattering: Hölder estimates and optimal Sobolev estimates for radial potentials ⋮ A New Convergent Algorithm to Approximate Potentials from Fixed Angle Scattering Data ⋮ Fixed Angle Scattering: Recovery of Singularities and Its Limitations ⋮ Born approximation for the magnetic Schrödinger operator ⋮ The Born approximation in the three-dimensional Calderón problem

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