Browsing Analysis of Partial Differential Equations (APDE) by Author "Caro, P."

Now showing items 1-9 of 9

    • The Calderón problem with corrupted data 

      Caro, P.; García, A. (2017-01)
      We consider the inverse Calderón problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, ...

    • Correlation imaging in inverse scattering is tomography on probability distributions 

      Caro, P.; Helin, T.; Kujanpää, A.; Lassas, M. (2018-12-04)
      Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments ...

    • Determination of convection terms and quasi-linearities appearing in diffusion equations 

      Caro, P.; Kian, Y. (2018-12)
      We consider the highly nonlinear and ill posed inverse problem of determining some general expression appearing in the a diffusion equation from measurements of solutions on the lateral boundary. We consider both linear ...

    • Global Uniqueness for The Calderón Problem with Lipschitz Conductivities 

      Caro, P.; Rogers, K.M. (2016-01-01)
      We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three- and four-dimensional cases, this confirms a conjecture of ...

    • Inverse scattering for a random potential 

      Caro, P.; Helin, T.; Lassas, M. (2016-05)
      In this paper we consider an inverse problem for the $n$-dimensional random Schrödinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ...

    • The observational limit of wave packets with noisy measurements 

      Caro, P.; Meroño, C. (2019)
      The authors consider the problem of recovering an observable from certain measurements containing random errors. The observable is given by a pseudodifferential operator while the random errors are generated by a Gaussian ...

    • Rotational smoothing 

      Caro, P.; Meroño, C.; Parissis, I. (2022-01-05)
      Rotational smoothing is a phenomenon consisting in a gain of regularity by means of averaging over rotations. This phenomenon is present in operators that regularize only in certain directions, in contrast to operators ...

    • Scattering with critically-singular and δ-shell potentials 

      Caro, P.; García, A. (2019)
      The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz ...

    • Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane 

      Caro, P.; Rogers, K. (2018-12)
      For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ...