40 citations · 73 across the 20 of their papers we have counts for
25 papers
Unique continuation at infinity for Schrödinger equations with Reverse Hölder Potentials
Blair Davey
In this article, we study unique continuation properties at infinity for solutions to generalized Schrödinger equations with potential functions that belong to the reverse Hölder c…
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, $\…
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 inf…
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…
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…
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…
On Landis' conjecture in the plane for potentials with growth
Blair Davey
We investigate the quantitative unique continuation properties of real-valued solutions to Schrödinger equations in the plane with potentials that exhibit growth at infinity. More…
Variable-coefficient parabolic theory as a high-dimensional limit of elliptic theory
Blair Davey, Mariana Smit Vega Garcia
This paper continues the study initiated in [B. Davey, Parabolic theory as a high-dimensional limit of elliptic theory, Arch Rational Mech Anal 228 (2018)], where a high-dimensiona…
Exponential Decay Estimates for Fundamental Matrices of Generalized Schrödinger Systems
Blair Davey, Joshua Isralowitz
In this article, we investigate systems of generalized Schrödinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matri…
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…
Landis' conjecture for general second order elliptic equations with singular lower order terms in the plane
Blair Davey, Jenn-Nan Wang
In this article, we study the order of vanishing and a quantitative form of Landis' conjecture in the plane for solutions to second-order elliptic equations with variable coefficie…
Quantitative uniqueness of solutions to second order elliptic equations with singular potentials in two dimensions
Blair Davey, Jiuyi Zhu
In this article, we study the vanishing order of solutions to second order elliptic equations with singular lower order terms in the plane. In particular, we derive lower bounds fo…
Quantitative uniqueness of solutions to second order elliptic equations with singular lower order terms
Blair Davey, Jiuyi Zhu
In this article, we study the quantitative uniqueness of solutions to second order elliptic equations with singular lower order terms. We quantify the strong unique continuation pr…
Fundamental matrices and Green matrices for non-homogeneous elliptic systems
Blair Davey, Jonathan Hill, Svitlana Mayboroda
In this paper, we establish existence, uniqueness, and scale-invariant estimates for fundamental solutions of non-homogeneous second order elliptic systems with bounded measurable…
The Landis Conjecture for variable coefficient second-order elliptic PDES
Blair Davey, Carlos Kenig, Jenn-Nan Wang
In this work, we study the Landis conjecture for second-order elliptic equations in the plane. Precisely, assume that is a measurable real-valued function satisfying $\|V\…
Parabolic theory as a high-dimensional limit of elliptic theory
Blair Davey
The aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts. This technique is demonstrated through new proofs of five important theor…
A Meshkov-type construction for the borderline case
Blair Davey
We construct functions that satisfy an elliptic eigenvalue equation of the form , where , and $…
A further quantification of the unique continuation properties of eigenfunctions of the magnetic Schrödinger operator
Blair Davey
We prove quantitative unique continuation results for solutions of in a neighborhood of infinity, where , and and are complex-va…
Sharp constructions of eigenfunctions of the magnetic Schrödinger operator
Blair Davey
We prove sharpness of quantitative unique continuation results for solutions of $-Δu + W\cdot \nabla u + V u = \la u$, where $\la \in \C$ and and are complex-valued decayin…