6 papers
Fractional Vector Calculus and the Fractional Maxwell's Equations
Giovanni Covi, Ruirui Wu
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…
An inverse problem for fractional random walks on finite graphs
Giovanni Covi, Matti Lassas
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity γ is defined. Our data consists in a sequence of partial observations of a fra…
Propagation of singularities and inverse problems for the viscoacoustic wave equation
Giovanni Covi, Maarten de Hoop, Mikko Salo
We study an inverse problem for the viscoacoustic wave equation, an integro-differential model describing wave propagation in viscoacoustic media with memory in the leading order t…
The higher-order fractional Schrödinger equation with nonlinear local perturbations: Uniqueness
Giovanni Covi, Ru-Yu Lai, Lili Yan
We study the higher-order fractional Schrödinger equation with local nonlinear perturbations and investigate both the forward and inverse problems. We establish both the Sobolev $…
Partial data stability for the inverse fractional conductivity problem
Giovanni Covi, Antti Kujanpää, Jesse Railo
The classical Calderón problem with partial data is known to be log-log stable in some special cases, but even the uniqueness problem is open in general. We study the partial data…
Geometrical optics for the fractional Helmholtz equation and applications to inverse problems
Giovanni Covi, Maarten de Hoop, Mikko Salo
In this paper we construct a parametrix for the fractional Helmholtz equation making use of geometrical optics solutions. We show that the…