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Seminar on New Results in Nonlinear Partial Differential Equations: A Publication of the Max-Planck-Institut fur Mathematik, Bonn - 1 edition

Seminar on New Results in Nonlinear Partial Differential Equations: A Publication of the Max-Planck-Institut fur Mathematik, Bonn (ISBN10: 332285051X; ISBN13: 9783322850515)
ISBN13: 978-3322850515
ISBN10: 332285051X

Summary: Recent years have seen a tremendous growth of interest in non-linear partial differential equations_ Yau's solution of the Calabi conjecture and more recently Schoen's solution of the Yamabe problem and Wente's counter-example of the Hopf conjecture have been a great stimulus to geometric P.D.E .. Applied P.D.E. has also seen great progress. The "year" in P.D.E., January-September 1984 at the Max-Planck-I nstitute was dedicated to bringing together some of the leaders in several fields of P.D.E
.. We preferred a seminar focused not on a given very specific area but one which cuts across boundaries of research interests. We hoped to have a snapshot of some of the more important recent devel opments in non-linear P.D.E .. The current volume contains some of the results reported upon in this seminar. From Henry Wente, in geometric P.D.E., we have new toroidal counter-examples to Hopf's conjecture, and, due to Uwe Abresch, a further development of these ideas. Sergiu Klainerman's global existence result for the non-linear Klein-Gordon equation in four space-time dimensions, achieved while at Max Planck, is included. Vince Moncrief presents his global existence result for the Yang-Mills equation in Min kowski space time. All of these results answer important and outstanding questions."
...show more
Summary: Recent years have seen a tremendous growth of interest in non-linear partial differential equations_ Yau's solution of the Calabi conjecture and more recently Schoen's solution of the Yamabe problem and Wente's counter-example of the Hopf conjecture have been a great stimulus to geometric P.D.E .. Applied P.D.E. has also seen great progress. The "year" in P.D.E., January-September 1984 at the Max-Planck-I nstitute was dedicated to bringing together some of the leaders in several fields of P.D.E .. We preferred a seminar focused not on a given very specific area but one which cuts across boundaries of research interests. We hoped to have a snapshot of some of the more important recent devel opments in non-linear P.D.E .. The current volume contains some of the results reported upon in this seminar. From Henry Wente, in geometric P.D.E., we have new toroidal counter-examples to Hopf's conjecture, and, due to Uwe Abresch, a further development of these ideas. Sergiu Klainerman's global existence result for the non-linear Klein-Gordon equation in four space-time dimensions, achieved while at Max Planck, is included. Vince Moncrief presents his global existence result for the Yang-Mills equation in Min kowski space time. All of these results answer important and outstanding questions."...show less

Edition/Copyright: 1
Cover: Paperback
Publisher: GWV Vieweg Verlag
Published: 02/13/2012
International: No



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