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

Chapter Page number
1 - Morse Inequalities and estimates for the number of solutions of nonlinear equations (pdf 1.21 MB)
EN Dancer
1
2 - Minimum problems for nonconvex integrals (pdf 1.07 MB)
Nicola Fusco
14
3 - Regularity for Solutions to Obstacle problems (pdf 451.86 KB)
JH Michael
29
4 - On sufficient conditions for Optimality (pdf 564.27 KB)
S Rolewicz
38
5 - Isolated Singularities for Extrema of Geometric Variational Problems (pdf 328.63 KB)
Leon Simon
46
6 - Hamiltonian Systems with Monotone trajectories (pdf 999.3 KB)
John Toland
51
7 - Boundary value problems for fully nonlinear elliptic equations (pdf 1.36 MB)
Neil S Trudinger
65
8 - Smooth foliations generated by functions of least gradient (pdf 518.61 KB)
William P Ziemer
84
9 - Harmonic Morphisms onto Riemann surfaces - some classification results (pdf 890.77 KB)
Paul Baird
91
10 - W(2,p) Regularity for varifolds with mean curvature (pdf 406.85 KB)
John Duggan
101
11 - Flow by mean curvature of convex surfaces into spheres (pdf 442.82 KB)
Gerhard Huisken
107
12 - Minimising curvature - A higher dimensional analogue of the plateau problem (pdf 880.13 KB)
John Hutchinson
113
13 - A semilinear elliptic boundary-value problem describing small patches of vorticity in an otherwise irrotational flow (pdf 967.36 KB)
Grant Keady
123
14 - Power concavity of solutions of dirichelet problems (pdf 316.99 KB)
Alan Kennington
133
15 - Asyptotically stable solutions of the navier-stokes equations and its galerkin approximations (pdf 913.15 KB)
Peter E Kloeden
137
16 - Quenching of solutions of evolution equations (pdf 460.97 KB)
Gary M Lieberman
151
17 - Some remarks on numerical methods for nonlinear heat squations with near singular specific heats (pdf 681.11 KB)
Anthony Miller
158
18 - Phase Retrieval as a nonlinear ill-posed problem (pdf 782.27 KB)
GN Newsam
168
19 - On a elliptic boundary value problem with mixed non-linear boundary conditions (pdf 849.09 KB)
AJ Pryde
177
20 - Slow steady flows of viscoelastic liequids with constitutive equations of maxwell or jeffreys type (pdf 280.73 KB)
Michale Rendary
191
21 - Ultrapowers in the lipschitz and uniform classification of banach spaces (pdf 503.06 KB)
Ian Roberts
195
22 - A remark on fully nonlinear, concave elliptic equations (pdf 420.92 KB)
Friedmar Schulz
202
23 - Non-Linear Characterizations of superflexive spaces (pdf 612.21 KB)
S Swaminathan
208
24 - Some recent results on the equatino of prescribed gauss curvature (pdf 507.22 KB)
John IE Urbas
215
25 - Existence via interior estimates for second order parabolic equations (pdf 897.96 KB)
John van der Hoek
221
26 - The Dirichlet problem for the minimal surface equation (pdf 557.61 KB)
Graham Williams
233
27 - Iterative methods for some large scale generalized equations (pdf 703.02 KB)
R S Womersley
240
28 - Best approximation operators in functional analysis (pdf 1.24 MB)
David Yost
249