Related papers: The Calder\'on Problem For The Fractional Magnetic…
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
In this paper we show, in dimension n >=3, that knowledge of the Cauchy data for the Schroedinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic…
In this paper we study an inverse problem for fractional anisotropic conductivity. Our nonlocal operator is based on the well-developed theory of nonlocal vector calculus, and differs substantially from other generalizations of the…
In this paper we derive Carleman estimates for the fractional relativistic operator. We consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity of certain energy functionals…
This licentiate thesis is concerned with an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, for compactly supported potentials $A\in W^{1,\infty}(\bar{\mathbb{R}^3_{-}},\R^3)$ and $q \in…
We study the inverse problem of determining the magnetic field and the electric potential entering the Schr\"odinger equation in an infinite 3D cylindrical domain, by Dirichlet-to-Neumann map. The cylindrical domain we consider is a closed…
We consider the Gel'fand-Calder\'on problem for a Schr\"odinger operator of the form $-(\nabla + iA)^2 + q$, defined on a ball $B$ in $\mathbb R^3$. We assume that the magnetic potential $A$ is small in $W^{s,3}$ for some $s>0$, and that…
We study an analog of the anisotropic Calder\'on problem for fractional Schr\"odinger operators $(-\Delta_g)^\alpha + V$ with $\alpha \in (0,1)$ on closed Riemannian manifolds of dimensions two and higher. We prove that the knowledge of a…
In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be…
We give a procedure for reconstructing a magnetic field and electric potential from boundary measurements related to the magnetic Schroedinger operator in three and higher dimensions.
We consider the fractional anisotropic Calder\'on problem for the nonlocal parabolic equation $(\partial_t -\Delta_g)^s u=f$ ($0<s<1$) on closed Riemannian manifolds. More concretely, we can determine the Riemannian manifold $(M,g)$ up to…
We investigate the Calder\'on problem for the fractional Schr\"odinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior…
It is well known from the work of Caffarelli and Silvestre that the fractional Laplacian $(-\Delta_x)^{\frac{\sigma}{2}}$ for $\sigma \in (0,2)$ can be obtained as a Dirichlet-to-Neumann map through an extension problem to the upper half…
We study inverse boundary problems for the magnetic Schr\"odinger operator with H\"older continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n greater…
We study the Dirichlet to Neumann operator of the $\overline{\partial}$-Neumann problem, and the relation between the $\overline{\partial}$-Neumann boundary conditions and the Dirichlet to Neumann operator.
The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a…
We study both the Riemannian and Lorentzian Calder\'on problem when a family of Dirichlet-to-Neumann maps are given for an open set of magnetic/electromagnetic potentials. For the Riemannian version, by allowing small perturbations of the…
We study an inverse boundary value problem with partial data in an infinite slab in $\mathbb{R}^{n}$, $n\geq 3$, for the magnetic Schr\"{o}dinger operator with an $L^{\infty}$ magnetic potential and an $L^{\infty}$ electric potential. We…
We consider a fractional variant of Maxwell's equations, where the electric and magnetic fields are modeled as two-point fields. To formulate the system, we introduce a fractional curl operator that is compatible with the fractional…
In the very influential paper \cite{CS07} Caffarelli and Silvestre studied regularity of $(-\Delta)^s$, $0<s<1$, by identifying fractional powers with a certain Dirichlet-to-Neumann operator. Stinga and Torrea \cite{ST10} and Gal\'e, Miana…