The Dirichlet problem is of central importance in both applied and abstract potential theory. We prove the (perhaps surprising) result that the existence of solutions in the general case is an… (More)

The existence and uniqueness properties for extremal mappings with smallest weighted L distortion between annuli and the related Grötzsch type problems are discussed. An interesting critical phase… (More)

We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the MilmanPettis theorem that uniformly… (More)

Here we show, contrary to the classical supposition, that a process for generating symbols according to some probability distribution need not, with any likelihood, produce a given finite text in any… (More)

This paper begins an analysis of the real line using an inconsistencytolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use… (More)

Two weakenings of the anti-Specker property—a principle of some significance in constructive reverse mathematics—are introduced, examined, and in one case applied, within Bishop-style constructive… (More)

In this chapter we suggest new models for the study of deformations of elastic media through the minimization of distortion functionals. This provides a “holistic” approach to this problem and a… (More)