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" Seminar on New Results in Nonlinear Partial Differential Equations "
by Anthony J. Tromba.
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BL
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577159
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b406378
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Tromba, Anthony J.
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| Title & Author
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Seminar on New Results in Nonlinear Partial Differential Equations : A Publication of the Max-Planck-Institut für Mathematik, Bonn /\ by Anthony J. Tromba.
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| Publication Statement
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Wiesbaden :: Vieweg+Teubner Verlag,, 1987.
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| Series Statement
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Aspects of Mathematics / Aspekte der Mathematik,; 10
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| ISBN
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9783322850492
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: 9783322850515
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| Contents
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Twisted Tori of Constant Mean Curvature in R3 -- Old and New Doubly Periodic Solutions of the Sinh-Gordon Equation -- Global Existence of Small Amplitude Solutions to Nonlinear Klein-Gordon Equations in Four Space-Time Dimensions -- Global Existence of Solutions of the Yang-Mills Equations in Minkowski Spacetime -- Nonlinear Stability in Fluids and Plasmas -- Lane-Emden Equations and Related Topics in Nonlinear Elliptic and Parabolic Problems -- Parabolicity and the Liouville Property on Complete Riemannian Manifolds -- Global Analysis and Teichmüller Theory.
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| Abstract
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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.
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Engineering.
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SpringerLink (Online service)
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