# Miniconference on nonlinear analysis

## Preface

This volume contains the proceedings of a miniconference on nonlinear analysis held at the Australian National University in July 1984, at the Centre for Mathematical Analysis. It is divided into two parts. The first consists of reports of expository lectures. The second is devoted to research reports communicated at the conference.

We gratefully acknowledge the support of the contributors to this volume as well as the excellent typing assistance of Marilyn, Dorothy and Norma. We would especially also like to thank Jim Michael for his participation and his agreement to have these proceedings dedicated to him.

## Dedication

On December 31, 1983, Dr JH Michael retired from his academic duties at the University of Adelaide. He has had a great deal of influence on the course of Mathematics, and in partuclar Analysis, in Australia for quite some time. Not only has he contributed significant works of his own but has also supervised several graduate students who have gone on to successful mathematical careers. Four of these former students (AU Kennington, LM Simon, J van der Hoek and GH Williams) also presented talks at this miniconference and many of the other speakers have had contact with Michael’s work.

Jim Michael completed his Ph.D. at the University of Adelaide in 1956 under the supervision of G Szekeres on a topic concerning Cauchy’s Integral Theorem and it’s applications. Prior to this he had attained his Bachelors degree which he partly completed while soldiering in the Australian Army. (In fact one examination was undertaken on a troop ship fending off bouts of seasickness!).

He then spent some time at the Universities of Manchester and Glasgow before returning to a lecturing position at Adelaide in 1958 where he remained (As Lecturer, Senior Lecturer, Reader, Professor and Reader) apart from study tours until his retirement. In addition to the work on Cauncy’s integral theorem he also made significant contributions to problems in the invariance of domains, approximation of general surfaces by Lipschitz graphs and more recently in the field of partial differential equations. He was elected as a Fellow of the Australian Academy of Sienc3s in 1973. Jim Michael’s work, while perhaps not large in volume, has always been very thorough and in several cases has presented new ideas which have turned out to be very significant in the later developments of the theory. These include in particular his study of LIpschitz approximations of variational integrals [11], his fundamental apper with Leon Simon on Sobolev inequalities on submanifolds [20] and his innovative approach to elliptic equations through interior estimates [15]. Although he has retired from academic duti3s he has not retired from research as can be seen from the appear presented by him at this conference.

## Contents

## Printed copy

## Volume

## Date

## Venue

## Copyright

First published in Australia 1985

© Centre for Mathematical Analysis,

The Australian National University

CANBERRA ACT 0200

AUSTRALIA

This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.

Neil S Trudinger, Graham H Williams

Miniconference on nonlinear analysis

Canberra, July 5-7, 1984)

ISBN 0 86784 509 0