Zobrazeno 1 - 10
of 75
pro vyhledávání: '"Davey, Blair"'
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 intersections with Lipschitz images, we ask whether these sets intersect wi
Externí odkaz:
http://arxiv.org/abs/2407.04837
Autor:
Davey, Blair
We investigate the quantitative unique continuation properties of real-valued solutions to Schr\"odinger equations in the plane with potentials that exhibit growth at infinity. More precisely, for equations of the form $\Delta u - V u = 0$ in $\mathb
Externí odkaz:
http://arxiv.org/abs/2305.05088
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-dimensional limiting technique was developed and used to prove certain parabolic
Externí odkaz:
http://arxiv.org/abs/2304.10731
Autor:
Davey, Blair, Isralowitz, Joshua
In this article, we investigate systems of generalized Schr\"odinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matrices and then prove sharp upper and lower exponential decay estimates
Externí odkaz:
http://arxiv.org/abs/2207.05790
Autor:
Davey, Blair, Taylor, Krystal
The Besicovitch projection theorem states that if a subset $E$ of the plane has finite length in the sense of Hausdorff measure and is purely unrectifiable (so its intersection with any Lipschitz graph has zero length), then almost every orthogonal p
Externí odkaz:
http://arxiv.org/abs/2104.00826
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 $\Delta u + W \cdot \nabla u = 0$ in $\mathbb{R}^2$, where $W = W_1 + i W_2
Externí odkaz:
http://arxiv.org/abs/2004.00157
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, the Favard length of a set is proportional to the probability that a nee
Externí odkaz:
http://arxiv.org/abs/2003.03620
Autor:
Davey, Blair
We investigate the quantitative unique continuation properties of solutions to second order elliptic equations with singular lower order terms. The main theorem presents a quantification of the strong unique continuation property for $\Delta + V$. Th
Externí odkaz:
http://arxiv.org/abs/1903.04021
Autor:
Davey, Blair
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 the operator, we establish quantitative forms of Landis' conjecture. Of
Externí odkaz:
http://arxiv.org/abs/1809.01520
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 step towards proving a quantitative version of Landis' conjecture by e
Externí odkaz:
http://arxiv.org/abs/1808.09420