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Descripción
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| We prove that in dimension $n \ge 2$ the main singularities of a complex potential $q$ having a certain a priori regularity are contained in the Born approximation $q_\theta$ constructed from fixed angle scattering data. Moreover, ${q-q_\theta}$ can be up to one derivative more regular than $q$ in the Sobolev scale. In fact, this result is optimal. We construct a family of compactly supported and radial potentials for which it is not possible to have more than one derivative gain. Also, these functions show that for $n>3$, the maximum derivative gain can be very small for potentials in the Sobolev scale not having a certain a priori level of regularity which grows with the dimension. | |
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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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Siam Journal on Mathematical Analysis |
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ISSN
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0036-1410 |
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Factor de impacto JCR
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1,528 |
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Información de impacto
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Volumen
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50 |
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DOI
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10.1137/18M1164871 |
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Número de revista
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5 |
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Desde la página
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5616 |
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5636 |
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SIN MES |
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Ranking
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