Miniconference on Operator Theory and Partial Differential Equations

Canberra, July 21-22, 1983

Volume 5 in the Proceedings of the Centre for Mathematical Analysis

Preface

This volume contains the proceedings of a miniconference on operator theory and partial differential equations held at the Australian National University in July, 1983, under the sponsorship of the Centre for Mathematical Analysis. It is divided into two parts. The first consists of reports of one hour expository lectures. The second is devoted to half our research reports presented at the conference.

We gratefully acknowledge the support of contributors to this volume, as well as the superb organizational assistance of our secretary, Marilyn Gray, and the excellent typing of Dorothy Nash.

Brian Jefferies, Alan McIntosh
(Editors)

Contents

Preface	2
Part I, Expository Lectures
Dilations preserving a bound on the norm of an operator Chandler Davis	3
Spectral properties of certain stiff problems in elasticity and acoustics, part II G. Geymonat and E. Sanchez-Palencia	15
Box maximal functions Alberto Torchinsky	39
Part II, Research Reports
The existence of maximal surfaces R. Bartnik	47
The group of invertible elements of certain Banach algebras of operators on Hilbert space A.L. Carey	52
The Dirichlet problem for a linear elliptic equation in a half space with L2-boundary data J. Chabrowski	61
Boolean algebras of projections in locally convex spaces Peter G. Dodds	67
Computing Fourier and Laplace transforms by means of power series evaluation Sven-Å Gustafson	77
C1,1-regularity of solutions to variational inequalities Gerhard Huisken	85
Weakly integrable semigroups Brian Jefferies	91
The inheritance of concavity by solutions of boundary value problems A.U. Kennington	98
Some problems of spectral theory Igor Kluvánek	103
Interpolation in Orlicz and Sobolev-Orlicz spaces Miroslav Krbec	109
Square roots of operators and applications to hyperbolic P.D.E.'s Alan McIntosh	124
Riesz capacity and the approximation of Sobolev functions by smooth functions J.H. Michael	137
A linearized elliptic free boundary value problem A.J. Pryde	140
Some problems of spectral theory Werner Ricker	145
The iterated Galerkin method for integral equations of the second kind I.H. Sloan	153