6 papers
A Quantification of a Besicovitch Nonlinear Projection Theorem via Multiscale Analysis
Blair Davey, Krystal Taylor
The Besicovitch projection theorem states that if a subset of the plane has finite length in the sense of Hausdorff measure and is purely unrectifiable (so its intersection wit…
Improved quantitative unique continuation for complex-valued drift equations in the plane
Blair Davey, Carlos Kenig, Jenn-Nan Wang
In this article, we investigate the quantitative unique continuation properties of complex-valued solutions to drift equations in the plane. We consider equations of the form $Δu +…
Upper and lower bounds on the rate of decay of the Favard curve length for the four-corner Cantor set
Laura Cladek, Blair Davey, Krystal Taylor
The Favard length of a subset of the plane is defined as the average of its orthogonal projections. This quantity is related to the probabilistic Buffon needle problem; that is, th…
Quantitative unique continuation for Schrödinger operators
Blair Davey
We investigate the quantitative unique continuation properties of solutions to second order elliptic equations with singular lower order terms. The main theorem presents a quantifi…
On Landis' conjecture in the plane for some equations with sign-changing potentials
Blair Davey
In this article, we investigate the quantitative unique continuation properties of real-valued solutions to elliptic equations in the plane. Under a general set of assumptions on t…
On Landis' conjecture in the plane when the potential has an exponentially decaying negative part
Blair Davey, Carlos Kenig, Jenn-Nan Wang
In this article, we continue our investigation into the unique continuation properties of real-valued solutions to elliptic equations in the plane. More precisely, we make another…