The first two chapters contain introductory courses. Chapter 1 presents the theory of Sobolev-
type spaces Hs (s∈ R) on Rn, on a smooth closed manifold, and on a smooth bounded …

THE DIRICHLET PROBLEM FOR ELLIPTIC EQUATIONS WITH DRIFT TERMS Page 1 Pubi.
Mat. 45 (2001), 199-217 THE DIRICHLET PROBLEM FOR ELLIPTIC EQUATIONS WITH DRIFT …

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 …

We consider divergence form elliptic operators $ L={-}\mathrm {div} A (x)\nabla $, defined in
the half space $\mathbb {R}^{n+ 1} _+ $, $ n\geq 2$, where the coefficient matrix $ A (x) $ is …

We consider divergence form elliptic operators of the form L=− divA (x)∇, defined in Rn+
1={(x, t)∈ Rn× R}, n⩾ 2, where the L∞ coefficient matrix A is (n+ 1)×(n+ 1), uniformly elliptic …

We consider second order elliptic divergence form systems with complex measurable
coefficients A that are independent of the transversal coordinate, and prove that the set of A …

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 …

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 …