文档介绍：Nassif Ghoussoub
Self-dual Partial Differential
Systems and Their
Variational Principles
123
Nassif Ghoussoub
University of British Columbia
Department of Mathematics
Vancouver BC V6T 1Z2
Canada
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ISSN: 1439-7382
ISBN: 978-0-387-84896-9 e-ISBN: 978-0-387-84897-6
DOI: -0-387-84897-6
Library of Congress Control Number: 2008938377
Mathematics Subject Classification (2000): 46-xx, 35-xx
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To Mireille.
Preface
How to solve partial differential systems pleting the square. This could well
have been the title of this monograph as it grew into a project to develop a sys-
tematic approach for associating suitable nonnegative energy functionals to a large
class of partial differential equations (PDEs) and evolutionary systems. The minima
of these functionals are to be the solutions we seek, not because they are critical
points (., from the corresponding Euler-Lagrange equations) but from also be-
ing zeros of these functionals. The approach can be traced back to Bogomolnyi’s
trick of “completing squares” in the basic equations of quantum field theory (.,
Yang-Mills, Seiberg-Witten, Ginzburg-Landau, etc.,), which allows for