10 papers
Failure of dimension drop for harmonic measure on Ahlfors regular flat boundaries
Yingying Cai, Cole Jeznach, Xavier Tolsa
We develop an -adic modification of the construction of David-Jeznach-Julia for compact subsets of the real line for which harmonic measure for the…
Failure of dimension drop for harmonic measure on Ahlfors regular boundaries of dimension close to
Yingying Cai, Cole Jeznach, Xavier Tolsa
For every we construct a compact -Ahlfors regular set for which harmonic measure of with pole at infinity is comparable to $\m…
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, $\…
Elliptic unique continuation below the Lipschitz threshold
Cole Jeznach
In this article, we investigate unique continuation principles for solutions of uniformly elliptic equations of the form when is less regula…
Singular set estimates for solutions to elliptic equations in higher co-dimension
Max Engelstein, Cole Jeznach, Yannick Sire
Recent advances in quantitative unique continuation properties for solutions to uniformly elliptic, divergence form equations (with Lipschitz coefficients) has led to a good unders…
On the number of nodal domains of homogeneous caloric polynomials
Matthew Badger, Cole Jeznach
We investigate the minimum and maximum number of nodal domains across all time-dependent homogeneous caloric polynomials of degree in (space $\…
Small constant uniform rectifiability
Cole Jeznach
We provide several equivalent characterizations of locally flat, -Ahlfors regular, uniformly rectifiable sets in with density close to for any dimension $…
Cantor sets with absolutely continuous harmonic measure
Guy David, Cole Jeznach, Antoine Julia
We construct Ahlfors regular Cantor sets of small dimension in the plane, such that the Hausdorff measure on is equivalent to the harmonic measure associated to its complem…
Non-local distance functions and geometric regularity
Max Engelstein, Cole Jeznach, Svitlana Mayboroda
We establish the equivalence between the regularity (rectifiability) of sets and suitable estimates on the oscillation of the gradient for smooth non-local distance functions. A pr…
A well-posed surface currents and charges system for electromagnetism in dielectric media
M. Ganesh, S. C. Hawkins, C. Jeznach +1
The free space Maxwell dielectric problem can be reduced to a system of surface integral equations (SIE). A numerical formulation for the Maxwell dielectric problem using an SIE sy…