Miniconference on Partial Differential Equations

Canberra, July 9-10, 1981

Volume 1 in the Proceedings of the Centre for Mathematical Analysis

Preface

This volume contains the proceedings of a miniconference on partial differential equations held at the Australian National University in July, 1981, under the sponsorship of the Mathematical Sciences Research Centre. It is divided into two parts. The first consists of reports of expository lectures. The second is devoted to brief research reports communicated at the conference.

We gratefully acknowledg the support of the contributors to this volume as well as the excellent typing assistance of Anna Zalucki. Publication of these proceedings is supported by the Commonwealth Special Research Centre for Mathematical Analysis at the Australian National University.

P.F. Price, L.M. Simon, N.S. Trudinger
(Editors)

Contents

Preface	i
Part I, Expository Lectures
Elliptic equations in non-divergence form Neil S. Trudinger	1
Regularity at the boundary and removable singularities for solutions of quasilinear parabolic equations William P. Ziemer	17
The Hilbert transform on Lipschitz curves Ronald Coifman, Alan McIntosh and Yves Meyer	26
On isolated singularities of minimal surfaces Leon Simon	70
Part II, Research Reports
Singular and quasi-bounded functions associated with the heat equation J. Chabrowski and B. Thompson	101
Maximum principle for non-linear degenerate inequalities of parabolic type J. Chabrowski and R. Výborný	103
Solvability of some asymptotically homogeneous elliptic problems E.N. Dancer	106
Stefan problems John van der Hoek	112
Vector-valued polymeasures and perturbations of semigroups of operators Igor Kluvánek	118
High order properly elliptic boundary value problems with weakly smooth coefficients A.J. Pryde	124