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• W2750871581 abstract "We prove that in dimension $2 le n le 6$ the main singularities of a complex potential $q$ having some a priori regularity are contained in the Born approximation $q_B$ constructed from backscattering data. Moreover, ${q-q_B}$ can be up to one derivative more regular than $q$ in the Sobolev scale. Also, in dimension $2le n <infty$ we construct compactly supported, radial and real counterexamples showing that in general it is not possible to have more than one derivative gain. In fact, we show that the double dispersion operator can even have worse regularity than the potential, if $q$ has regularity below a certain level which grows with the dimension." @default.
• W2750871581 created "2017-09-15" @default.
• W2750871581 creator A5013100948 @default.
• W2750871581 date "2017-09-03" @default.
• W2750871581 modified "2023-09-27" @default.
• W2750871581 title "Recovering the singularities of a potential from Backscattering data" @default.
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• W2750871581 hasPublicationYear "2017" @default.
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