Joel Nathe

collaborators

3 papers

math.AP2026

Recovery of a Null Form in the Wave Equation from Scattering Data

Joel Nathe

We use highly oscillatory geometric optics solutions to solve the inverse problem for the system \begin{equation} \square \begin{bmatrix} u^{(1)}\\ u^{(2)}\\ \vdots\\ u^{(n)}\end{b…

math.CA2026

Subharmonic Kernels and Energy Minimizing Measures, with Applications to the Flat Torus

Steven B. Damelin, Joel Nathe

We study the minimization of the energy integral $I_{K} (I^¼) = \int_{I^} c ◯ \int_{I^} c ◯ K (x, y) d I^¼ (x) d I^¼ (y)$ over all Borel probability measures $I^¼$ , where $(I^c ◯, I ¨ )$ is a compact connected m…

math.AP2026

The Recovery of Semilinear Potentials Satisfying Null Conditions From Scattering Data

Joel Nathe, AntÃ´nio SÃ¡ Barreto

We construct oscillatory solutions of fully semilinear wave equations in Minkowski space satisfying a null condition of the form $$\square u:=(-\partial_{x_0}^2 +\sum_{j=1}^n \part…