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 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 …

We study the properties of harmonic measure in semi-uniform domains. Aikawa and Hirata
showed in that, for John domains satisfying the capacity density condition (CDC), the …

The present paper concerns divergence form elliptic and degenerate elliptic operators in a
domain Ω⊂ R n, and establishes the equivalence between the uniform rectifiability of the …

In the recent work G. David, J. Feneuil, and the first author have launched a program
devoted to an analogue of harmonic measure for lower-dimensional sets. A relevant class of …

Dimension Drop for Harmonic Measure on Ahlfors Regular Boundaries Page 1 Potential
Analysis https://doi.org/10.1007/s11118-019-09796-6 Dimension Drop for Harmonic Measure on …

It is a well-known folklore result that quantitative, scale invariant absolute continuity (more
precisely, the weak-A∞ property) of harmonic measure with respect to surface measure, on …

The present paper, along with its companion [HMMTZ], establishes the correspondence
between the properties of the solutions of a class of PDEs and the geometry of sets in …

Let be a domain in RdC1, where d 1. It is known that if satisfies a corkscrew condition and@
is d-Ahlfors regular, then the following are equivalent:(a) a square function Carleson …

We study perturbation results for boundary value problems for second-order elliptic partial
differential equations, and the exponential decay of solutions to generalized Schr\" odinger …