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 …

Abstract Let Ω⊂ R n+ 1, n≥ 2 be a bounded open and connected set satisfying the
corkscrew condition with uniformly n-rectifiable boundary. In this paper we study the …

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 …

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 …

We establish a new theory of regularity for elliptic complex valued second order equations of
the form L= div A (∇⋅), when the coefficients of the matrix A satisfy a natural algebraic …

Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data
in Besov Spaces Page 1 MEMOIRS of the American Mathematical Society Volume 243 • …

We consider divergence form elliptic equations L u:=∇⋅(A∇ u)= 0 in the half space R+ n+
1:={(x, t)∈ R n×(0,∞)}, whose coefficient matrix A is complex elliptic, bounded and …

We prove that the Lp′-solvability of the homogeneous Dirichlet problem for an elliptic
operator L=− div A∇ with real and merely bounded coefficients is equivalent to the Lp …

We consider layer potentials associated to elliptic operators acting in the upper half-space
for, or more generally, in a Lipschitz graph domain, where the coefficient matrix is-and …

We prove that the solvability of the regularity problem in Lq.@/is stable under Carleson
perturbations. If the perturbation is small, then the solvability is preserved in the same Lq …