The double dispersion operator in backscattering: Hölder estimates and optimal Sobolev estimates for radial potentials

• Cristóbal J. Meroño ^[1]
  1. [1] Universidad Politécnica de Madrid

     Universidad Politécnica de Madrid

     Madrid, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 3, 2021, págs. 1175-1205
• Idioma: inglés
• DOI: 10.4171/rmi/1223
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study the problem of recovering the singularities of a potential q from backscattering data. In particular, we prove two new different estimates for the double dispersion operator Q2 of backscattering, the first nonlinear term in the Born series. In the first, by measuring the regularity in the Hölder scale, we show that there is a one derivative gain in the integrablity sense for suitably decaying potentials q∈Wβ,2(Rn) with β≥(n−2)/2 and n≥3. In the second, we give optimal estimates in the Sobolev scale for Q2(q) when n≥2 and q is radial. In dimensions 2 and 3 this result implies an optimal result of recovery of singularities from the Born approximation.