Add to ORKGMany 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 develop a version of elliptic theory, associated to a linear PDE, which ultimately yields a notion analogous to that of the harmonic measure, for sets of codimension higher than 1. To this end, we turn to degenerate elliptic equations. Let $\Gamma \subset \mathbb R^n$ be an Ahlfors regular set of dimension $d<n-1$ (not necessarily integer) and $\Omega = \mathbb R^n \setminus \Gamma$. Let $L = - {\rm div} A\nabla$ be a degenerate elliptic operator with measurable coefficients such that the ellipticity constants of the matrix $A$ are bounded from above and below by ...
summary:Let $F$ be a relatively closed subset of a Euclidean domain $\Omega$. We investigate when so...
We show optimal Lipschitz regularity for very weak solutions of the (measure-valued) elliptic PDE $-...
We prove estimates for the variation of the eigenvalues of uniformly elliptic operators with homogen...
Take an open domain $\Omega \subset \mathbb R^n$ whose boundary may be composed of pieces of differe...
76 pages.In 1977 the celebrated theorem of B.\, Dahlberg established that the harmonic measure is ab...
Abstract from public.pdf file.Dissertation supervisor: Dr. Steve Hoffmann.Includes vita.In this thes...
7 pagesInternational audienceWe introduce a new notion of a harmonic measure for a $d$-dimensional s...
116pagesTake an open domain Ω ⊂ R n whose boundary may be composed of pieces of different dimensions...
We study absolute continuity of harmonic measure with respect to surface measure on domains Ω that h...
We prove a structure theorem for any $n$-rectifiable set $E\subset\mathbb{R}^{n+1}, n \geq 1$, satis...
Thesis (Ph.D.)--University of Washington, 2018Harmonic/elliptic measure arises naturally in probabil...
We study the Hausdorff dimension of a certain Borel measure associated to a positive weak solution o...
AbstractWe study higher order elliptic operators with measurable coefficients acting on Euclidean do...
We study the Hausdorff dimension of a certain Borel measure associated to a positive weak solution o...
We study the Hausdorff dimension of a certain Borel measure associated to a positive weak solution o...
summary:Let $F$ be a relatively closed subset of a Euclidean domain $\Omega$. We investigate when so...
We show optimal Lipschitz regularity for very weak solutions of the (measure-valued) elliptic PDE $-...
We prove estimates for the variation of the eigenvalues of uniformly elliptic operators with homogen...
Take an open domain $\Omega \subset \mathbb R^n$ whose boundary may be composed of pieces of differe...
76 pages.In 1977 the celebrated theorem of B.\, Dahlberg established that the harmonic measure is ab...
Abstract from public.pdf file.Dissertation supervisor: Dr. Steve Hoffmann.Includes vita.In this thes...
7 pagesInternational audienceWe introduce a new notion of a harmonic measure for a $d$-dimensional s...
116pagesTake an open domain Ω ⊂ R n whose boundary may be composed of pieces of different dimensions...
We study absolute continuity of harmonic measure with respect to surface measure on domains Ω that h...
We prove a structure theorem for any $n$-rectifiable set $E\subset\mathbb{R}^{n+1}, n \geq 1$, satis...
Thesis (Ph.D.)--University of Washington, 2018Harmonic/elliptic measure arises naturally in probabil...
We study the Hausdorff dimension of a certain Borel measure associated to a positive weak solution o...
AbstractWe study higher order elliptic operators with measurable coefficients acting on Euclidean do...
We study the Hausdorff dimension of a certain Borel measure associated to a positive weak solution o...
We study the Hausdorff dimension of a certain Borel measure associated to a positive weak solution o...
summary:Let $F$ be a relatively closed subset of a Euclidean domain $\Omega$. We investigate when so...
We show optimal Lipschitz regularity for very weak solutions of the (measure-valued) elliptic PDE $-...
We prove estimates for the variation of the eigenvalues of uniformly elliptic operators with homogen...