5 papers
Optimal rates of decay at infinity for solutions to Schrödinger equations
Blair Davey, Cole Jeznach
We prove rates of decay at infinity for solutions to variable-coefficient Schrödinger equations of the form in cylinders,…
A frequency function approach to quantitative unique continuation for elliptic equations
Blair Davey
We investigate the quantitative unique continuation properties of solutions to second-order elliptic equations with lower-order terms. In particular, we establish quantitative form…
On Landis' conjecture in the plane for real-valued potentials with decay
Blair Davey
We investigate the quantitative unique continuation properties of real-valued solutions to planar Schrödinger equations with potential functions that exhibit pointwise decay at in…
Self-similar sets and Lipschitz graphs
Blair Davey, Silvia Ghinassi, Bobby Wilson
We investigate and quantify the distinction between rectifiable and purely unrectifiable 1-sets in the plane. That is, given that purely unrectifiable 1-sets always have null inter…
Fractional Parabolic Theory as a High-Dimensional Limit of Fractional Elliptic Theory
Blair Davey, Mariana Smit Vega Garcia
This paper continues the program that was initiated in \cite{Dav18} and continued in \cite{DSVG24}, where a high-dimensional limiting technique was developed and used to prove cert…