In the late 1950s and early 1960s, the work of De Giorgi [DeGi] and Nash [N], and then
Moser [Mo], initiated the study of regularity of solutions to divergence form elliptic equations …

We continue the development, by reduction to a first-order system for the conormal gradient,
of L 2 a priori estimates and solvability for boundary value problems of Dirichlet, regularity …

The present paper establishes the correspondence between the properties of the solutions
of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of …

Let,, be an open set with Ahlfors regular boundary that satisfies the corkscrew condition. We
consider a uniformly elliptic operator in divergence form associated with a matrix with real …

The recent years have seen a beautiful breakthrough culminating in a comprehensive
understanding of certain scale-invariant properties of n− 1 dimensional sets across analysis …

We consider a certain class of second order, variable coefficient divergence form elliptic
operators, in a uniform domain Ω with Ahlfors regular boundary, and we show that the A∞ …

We extend in two directions the notion of perturbations of Carleson type for the Dirichlet
problem associated to an elliptic real second-order divergence-form (possibly degenerate …

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 …

In this article we study two classical potential-theoretic problems in convex geometry. The
first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity …

In this paper, we continue the study of a class of second order elliptic operators of the form
L= div (A∇⋅) in a domain above a Lipschitz graph in R n, where the coefficients of the …