W. V. D. Hodge’s seminal work on harmonic integrals in the 1930’s (cf. [15]) has had a lasting influence and profound implications in analysis. One specific direction, potential theory in Riemannian… (More)

We identify a large class of constant (complex) coefficient, second order elliptic systems for which the Dirichlet problem in the upper-half space with data in Lp-based Sobolev spaces, 1 < p < ∞, of… (More)

A classical problem arising in fluid dynamics and electrodynamics is the determination of a vector field with prescribed divergence and curl. Such a vector field can be considered in the whole… (More)

∣ ∂Ω = g on ∂Ω. The situation when g ∈ Lp(∂Ω), f = 0 and nontangential maximal function estimates are sought for the solution has received a lot of attention. For example, [9], [19], [24], [50], [11]… (More)

We identify the optimal range of coefficients s, p for which differential forms with coefficients in the Sobolev space Ls(Ω) admit natural Hodge decompositions in arbitrary two and three dimensional… (More)

A basic prerequisite in the study of boundary value problems associated with a differential operator in a domain Ω is the availability of suitable trace and extension theorems. In the context when… (More)

In this paper we discuss a new approach and an extension of the results in [11] regarding transmission boundary value problems and spectral theory for singular integral operators on Lipschitz… (More)

We show that the boundedness of the Hardy-Littlewood maximal operator on a Köthe function space X and on its Köthe dual X′ is equivalent to the well-posedness of the X-Dirichlet and X′-Dirichlet… (More)

We consider Dirichlet and Poisson type problems for the Maxwell-Dirac operator IDk = d + δ + k dt· on a Lipschitz subdomain Ω of a smooth, Riemannian manifold M. The emphasis is on solutions of… (More)

Abstract. We explore the extent to which basic differential operators (such as Laplace-Beltrami, Lamé, Navier-Stokes, etc.) and boundary value problems on a hypersurface S in R can be expressed… (More)