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Descripción
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| We prove that in dimension n ?2 the main singularities of a complex potential q having a certain a priori regularity are contained in the Born approximation qB constructed from backscattering data. This is archived using a new explicit formula for the multiple dispersion operators in the Fourier transform side. We also show that q?qB be up to one derivative more regular than q in the Sobolev scale. On the other hand, we construct counterexamples showing that in general it is not possible to have more than one derivative gain, sometimes even strictly less, depending on the a priori regularity of q. | |
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Internacional
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Si |
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JCR del ISI
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Si |
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Título de la revista
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Journal of Differential Equations |
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ISSN
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0022-0396 |
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Factor de impacto JCR
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2,192 |
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Información de impacto
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Volumen
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266 |
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DOI
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10.1016/j.jde.2018.11.003 |
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Número de revista
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Desde la página
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6307 |
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Hasta la página
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6345 |
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Mes
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SIN MES |
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Ranking
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19 |