Miniconference on Analysis and Applications

Brisbane 1993

Volume 33 in the Proceedings of the Centre for Mathematics and its Applications

Preface

This volume represents the proceedings of the miniconference on "Analysis and Applications" held at The University of Queensland from the 20^th to the 23^rd of September 1993. The conference was sponsored by The Unit for Mathematical Analysis of The University of Queensland, the Centre for Mathematics and its Applications at Australian National University and The Australian Mathematical Society. Bevan Thompson and Neil Trudinger formed the Programme Committee while Bevan and Tim Cranny handled most of the organisational details.

The scope of the conference was very broad including Linear and Nonlinear Functional Analysis, Applications of Ordinary and Partial Differential Equations to questions in Analysis and Geometry, Harmonic Analysis, Numerical Analysis and Nonlinear Analysis in general. Indeed the scope was so great that it is impossible to summarize here other than to point out the pervading theme of nonlinear analysis and its applications, particularly in geometry.

Contributions for the proceedings were sought at the conference. Many, but not all, of the papers received were refereed. Most of the contributions are expository in nature, either surveying the author's recent work or aspects of a particular field in which the author works. One can see from the contributions the enormous range and depth of analysis currently being studied in Australasia.

The conference was a great success, blessed by good organisation, great weather and the invigorating presence of several overseas colleagues.

Gaven Martin and Bevan Thompson
(Editors)

Contents

Evolving Convex Hypersurfaces Ben Andrews	1
Rotating Drops Trapped between Parallel Planes Maria Athanassenas	25
Indefinite Integrals of Fuctions From Lp(R) Bolis Basit and Alan J. Pryde	29
Two Notes on Supercritical Problems on Long Domains E.N. Dancer	39
Shadowing and Approximation in Dynamical Systems P. Diamond, P. Kloeden and A. Pokrovskii	47
Multivalued Spatial Discretization of Dynamical Systems P. Diamond, P. Kloeden and A. Pokrovskii	61
Invariant Theory in Differential Geometry Michael Eastwood	71
On Mean Curvature Flow of Surfaces in Riemannian 3-Manifolds Klaus Ecker	79
Hopf Bifurcation of a Class of PDE's Xiangjian He and Zhuhan Jiang	89
Degenerate Holomorphic Mappings of Nondegenerate CR-Manifolds A.V. Isaev	99
Travelling Wave Solutions for a Drying Problem Miloš Ilic	107
The Maximum Principle for Degenerate Parabolic PDE's with Singularities Hitoshi Ishii	113
Compensated Compactness, Commutators and Hardy Spaces Chun Li	121
Representations of Functions in Sobolev Spaces in Terms of Finite Differences Wai-Lok Lo	133
Measurable Conformal Mappings in Space Gaven J. Martin	145
Formation of Singularities in Solutions of the Nonlinear Schrödinger Equation with Critical Power Nonlinearity Hayato Nawa	167
Transference from Lipschitz Graphs to Periodic Lipschitz Graphs Tao Qian	189
Monotone Convergent Methods for a Variational Inequality David E. Stewart and Steven J. Wright	195
Degenerate Monge-Ampère Equations in Algebraic Geometry Hajime Tsuji	209
Nonlinear Oblique Boundary Value Problems for Two Dimensional Hessian and Curvature Equations John Urbas	225
Integrable Systems and the Geometry of Differential Operators P.J. Vassiliou	239
Existence of a Potential by Kurzweil-Henstock Integration R. Výborný	251
Multiwell Problems and Restrictions on Microstructure Kewei Zhang	259