127 citations · 205 across the 19 of their papers we have counts for
4 papers · 1 filter
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…