In recent years, there has been a great deal of activity in the study of boundary value
problems with minimal smoothness assumptions on the coefficients or on the boundary of …

Let $ X $ be a metric space with doubling measure, and $ L $ be a non-negative, self-adjoint
operator satisfying Davies-Gaffney bounds on $ L^ 2 (X) $. In this article we present a theory …

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 …

Consider a second order divergence form elliptic operator L with complex bounded
measurable coefficients. In general, operators based on L, such as the Riesz transform or …

This paper presents two observability inequalities for the heat equation over×(0, T). In the
first one, the observation is from a subset of positive measure in×(0, T), while in the second …

For a family of second-order elliptic systems with rapidly oscillating periodic coefficients in a
$ C^{1,\alpha} $ domain, we establish uniform $ W^{1, p} $ estimates, Lipschitz estimates …

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 study boundary value problems for the time-harmonic form of the Maxwell equations, as
well as for other related systems of equations, on arbitrary Lipschitz domains in the three …

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 …