Zobrazeno 1 - 10
of 151
pro vyhledávání: '"Caro, Pedro"'
In this work, we investigate the quantitative estimates of the unique continuation property for solutions of an elliptic equation $\Delta u = V u + W_1 \cdot \nabla u + \hbox{div} (W_2 u)$ in an open, connected subset of $\mathbb{R}^d$, where $d \geq
Externí odkaz:
http://arxiv.org/abs/2411.19021
We determine the conductivity of the interior of a body using electrical measurements on its surface. We assume only that the conductivity is bounded below by a positive constant and that the conductivity and surface are Lipschitz continuous. To dete
Externí odkaz:
http://arxiv.org/abs/2401.06120
Autor:
Caro, Pedro, Ruiz, Alberto
Data-driven prediction in quantum mechanics consists in providing an approximative description of the motion of any particles at any given time, from data that have been previously collected for a certain number of particles under the influence of th
Externí odkaz:
http://arxiv.org/abs/2302.10553
We provide examples of periodic solutions (in both 2 and 3 dimension) of the Magnetohydrodynamics equations such that the topology of the magnetic lines changes during the evolution. This phenomenon, known as magnetic reconnection, is relevant for ph
Externí odkaz:
http://arxiv.org/abs/2209.09600
Publikováno v:
J. Differential Equations306(2022), 101--151
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 regularizing in all directions.
Externí odkaz:
http://arxiv.org/abs/2105.04926
Autor:
Caro, Pedro, Meroño, Cristóbal J.
Publikováno v:
SIAM J. Math. Anal. Vol. 52(5), 2020
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 white noise. The authors sho
Externí odkaz:
http://arxiv.org/abs/1909.11394
Autor:
Caro, Pedro, Garcia, Andoni
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 hypersurface. They study direct
Externí odkaz:
http://arxiv.org/abs/1906.05825
We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these two systems
Externí odkaz:
http://arxiv.org/abs/1903.03524
Autor:
Caro, Pedro, Rogers, Keith M.
For potentials $V\in L^\infty(\mathbb{R}^2,\mathbb{R})$ and $A\in W^{1,\infty}(\mathbb{R}^2,\mathbb{R}^2)$ with compact support, we consider the Schr\"odinger equation $-(\nabla +iA)^2 u+Vu=k^2u$ with fixed positive energy $k^2$. Under a mild additio
Externí odkaz:
http://arxiv.org/abs/1901.04814