Uniqueness for the inverse fixed angle scattering problem
| Autor: | María de la Cruz Vilela, Cristóbal J. Meroño, Alberto Ruiz, Carlos Castro, Juan Antonio Barceló, Teresa Luque |
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| Rok vydání: | 2018 |
| Předmět: |
Physics
Pure mathematics Scattering Applied Mathematics Operator (physics) Dimension (graph theory) Inverse 01 natural sciences 010305 fluids & plasmas 010101 applied mathematics Sobolev space symbols.namesake Mathematics - Analysis of PDEs 0103 physical sciences symbols FOS: Mathematics Beta (velocity) Uniqueness 0101 mathematics Schrödinger's cat Analysis of PDEs (math.AP) 35P25 35R30 35J05 |
| DOI: | 10.48550/arxiv.1811.03443 |
| Popis: | We present a uniqueness result in dimensions 3 for the inverse fixed angle scattering problem associated to the Schrödinger operator - Δ + q {-\Delta+q} , where q is a small real-valued potential with compact support in the Sobolev space W β , 2 {W^{\beta,2}} , with β > 0 . {\beta>0.} This result improves the known result [P. Stefanov, Generic uniqueness for two inverse problems in potential scattering, Comm. Partial Differential Equations 17 1992, 55–68], in the sense that almost no regularity is required for the potential. The uniqueness result still holds in dimension 4, but for more regular potentials in W β , 2 {W^{\beta,2}} , with β > 2 / 3 {\beta>2/3} . The proof is a consequence of the reconstruction method presented in our previous work, [J. A. Barceló, C. Castro, T. Luque and M. C. Vilela, A new convergent algorithm to approximate potentials from fixed angle scattering data, SIAM J. Appl. Math. 78 2018, 2714–2736]. |
| Databáze: | OpenAIRE |
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