Inversion of spherical means and the wave equation in even dimensions
D. Finch, M. Haltmeier, Rakesh
Abstract
We establish inversion formulas of the so called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball. We also find several formulas to recover initial data of the form (f,0) (or (0,g)) for the free space wave equation in even dimensions from the trace of the solution on the boundary of the ball, provided the initial data has support in the ball.
Create a lesson
Related papers
Positive normalized solutions for a singular regularized p(x)-Laplacian Dirichlet problem
Mustafa Avci
Regularity for axisymmetric Navier-Stokes with an Euler length
Peter Constantin, Mihaela Ignatova, Vlad Vicol
Existence of strong initial traces for stochastic conservation laws
Marko Erceg, Nikola Konatar, Kenneth Karlsen et al.
Asymptotics of nonlocal nonlinear Robin energies
Serena Dipierro, Giuseppe Spadaro, Enrico Valdinoci
Discontinuity of the Vlasov--Poisson Flow in LxpLv∞
Ke Chen, In-Jee Jeong, Quoc-Hung Nguyen et al.
Dense orbits for scale-invariant rotationally symmetric solutions of the 2D Euler equations
Ibrahim Suleiman