127 citations · 205 across the 19 of their papers we have counts for
26 papers
Recovering Sharp Conductivity Features in the Finite-Data Calderón Problem with Physics-Informed Neural Networks
Ali AlHadi Kalout, Pablo Tejerina-Pérez, Konstantin Karchev +5
Physics-informed neural networks (PINNs) have recently emerged as a promising framework for addressing the Calderón inverse problem from limited boundary data. In this work, we rev…
Robin Green Function Estimates and a Model of Mammalian Lungs
Guy David, Stefano Decio, Max Engelstein +3
The present paper establishes delicate properties of the Green function with Robin boundary conditions, in particular, elucidating the nature of the passage between the Dirichlet-l…
Periodic homogenization and harmonic measures
Guy David, Antoine Gloria, Svitlana Mayboroda +1
Since the seminal work of Kenig and Pipher, the Dahlberg-Kenig-Pipher (DKP) condition on oscillations of the coefficient matrix became a standard threshold in the study of absolute…
Dimension and structure of the Robin Harmonic Measure on Rough Domains
Guy David, Stefano Decio, Max Engelstein +2
The present paper establishes that the Robin harmonic measure is quantitatively mutually absolutely continuous with respect to the surface measure on any Ahlfors regular set in any…
The landscape function on
Guy David, Antoine Gloria, Svitlana Mayboroda
Consider the Schrödinger operator with non-negative iid random potential of strength . We prove existence and uniqueness of the associated landscape functi…
Small results for Dahlberg-Kenig-Pipher operators in sets with uniformly rectifiable boundaries
Guy David, Linhan Li, Svitlana Mayboroda
In the present paper, we consider elliptic operators in a domain bounded by a chord-arc surface with small enough constant, and whose coefficients $A…
An optimal partition problem for the localization of eigenfunctions
Guy David, Hassan Pourmohammad
We study the minimizers of a functional on the set of partitions of a domain into subsets of locally finite perimeter in , whose main term is $\sum_{j=1…
Carleson estimates for the Green function on domains with lower dimensional boundaries
Guy David, Linhan Li, Svitlana Mayboroda
In the present paper, we consider an elliptic divergence form operator in with and prove that its Green function is almost affine, in th…
Carleson measure estimates for the Green function
Guy David, Linhan Li, Svitlana Mayboroda
In the present paper, we consider an elliptic divergence form operator in the half-space and prove that its Green function is almost affine, or more precisely, that the normalized…
Green function estimates on complements of low-dimensional uniformly rectifiable sets
Guy David, Joseph Feneuil, Svitlana Mayboroda
It has been recently established by the first and third author that on uniformly rectifiable sets the Green function is almost affine in the weak sense, and moreover, in some scena…
Approximation of Green functions and domains with uniformly rectifiable boundaries of all dimensions
Guy David, Svitlana Mayboroda
The present paper establishes equivalence between uniform rectifiability of the boundary of a domain and the property that the Green function for elliptic operators is well approxi…
Sharp estimates for the integrated density of states in Anderson tight-binding models
Perceval Desforges, Svitlana Mayboroda, Shiwen Zhang +4
Recent work [G. David, M. Filoche, and S. Mayboroda, arXiv:1909.10558[Adv. Math. (to be published)]] has proved the existence of bounds from above and below for the Integrated Dens…
Good elliptic operators on Cantor sets
Guy David, Svitlana Mayboroda
It is well known that a purely unrectifiable set cannot support a harmonic measure which is absolutely continuous with respect to the Hausdorff measure of this set. We show that no…
Harmonic measure is absolutely continuous with respect to the Hausdorff measure on all low-dimensional uniformly rectifiable sets
G. David, S. Mayboroda
It was recently shown that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a domain with an dimensional uniformly rectifiable boundary,…
Elliptic theory in domains with boundaries of mixed dimension
Guy David, Joseph Feneuil, Svitlana Mayboroda
Take an open domain whose boundary may be composed of pieces of different dimensions. For instance, can be a ball on , minus one of its diam…
The landscape law for the integrated density of states
Guy David, Marcel Filoche, Svitlana Mayboroda
The present paper establishes non-asymptotic estimates from above and below on the integrated density of states of the Schrödinger operator , using a counting function for…
Square functions, non-tangential limits and harmonic measure in co-dimensions larger than one
Guy David, Max Engelstein, Svitlana Mayboroda
In this paper, we characterize the rectifiability (both uniform and not) of an Ahlfors regular set, E, of arbitrary co-dimension by the behavior of a regularized distance function…
A new elliptic measure on lower dimensional sets
Guy David, Joseph Feneuil, Svitlana Mayboroda
The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of dimensional sets across analysis, ge…
Localization of eigenfunctions via an effective potential
Douglas N. Arnold, Guy David, Marcel Filoche +2
We consider the localization of eigenfunctions for the operator $L=-\mbox{div} A \nabla + V$ on a Lipschitz domain and, more generally, on manifolds with and without boundary.…
Computing spectra without solving eigenvalue problems
Douglas Arnold, Guy David, Marcel Filoche +2
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An impor…
Dahlberg's theorem in higher co-dimension
Guy David, Joseph Feneuil, Svitlana Mayboroda
In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension…
Elliptic theory for sets with higher co-dimensional boundaries
Guy R. David, Joseph Feneuil, Svitlana Mayboroda
Many geometric and analytic properties of sets hinge on the properties of harmonic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to de…
Harmonic measure on sets of codimension larger than one
Guy David, Joseph Feneuil, Svitlana Mayboroda
We introduce a new notion of a harmonic measure for a -dimensional set in with , that is, when the codimension is strictly bigger than 1. Our measure is associated…
Effective confining potential of quantum states in disordered media
Douglas N. Arnold, Guy David, David Jerison +2
The amplitude of localized quantum states in random or disordered media may exhibit long range exponential decay. We present here a theory that unveils the existence of an effectiv…