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 …

In this paper we show uniqueness of the conductivity for the quasilinear Calderón's inverse
problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself …

Abstract Let E⊂ R n+ 1, n≥ 2, be a uniformly rectifiable set of dimension n. Then bounded
harmonic functions in Ω:= R n+ 1∖ E satisfy Carleson measure estimates and are ε …

Given any elliptic system with t-independent coefficients in the upper-half space, we obtain
representation and trace for the conormal gradient of solutions in the natural classes for the …

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 …

In this paper, we provide a new means of establishing solvability of the Dirichlet problem on
Lipschitz domains, with measurable data, for second order elliptic, nonsymmetric divergence …

Abstract Let Ω⊂ R n+ 1, n≥ 1, be a corkscrew domain with Ahlfors–David regular boundary.
In this article we prove that∂ Ω is uniformly n-rectifiable if every bounded harmonic function …

Abstract Let (X, d, μ, E) be a Dirichlet metric measure space satisfying a doubling condition
and supporting a scale-invariant L 2-Poincaré inequality. Assume that L is a non-negative …

The present paper establishes a certain duality between the Dirichlet and Regularity
problems for elliptic operators with t t-independent complex bounded measurable …

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 …