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Wave maps

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Nonlinear Partial Differential Equations in Geometry and Physics

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 29))

Abstract

In these lectures we outline the known results concerning existence, uniqueness, and regularity for the Cauchy problem for harmonic maps from (1 + m)-dimensional Minkowski space into a Riemannian target manifold, also known as α-models or wave maps. In particular, we mark the limits of the classical theory in high dimensions and trace recent developments in dimension m = 2, substantiating the conjecture that in this “conformai” case the Cauchy problem is well-posed in the energy space.

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Authors and Affiliations

  1. Mathematik, ETH-Zentrum, CH-8092, Zürich, Switzerland

    Michael Struwe

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  1. Michael Struwe
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996-1300, USA

    Garth Baker  & Alexandre Freire  & 

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© 1997 Springer Basel AG

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Struwe, M. (1997). Wave maps. In: Baker, G., Freire, A. (eds) Nonlinear Partial Differential Equations in Geometry and Physics. Progress in Nonlinear Differential Equations and Their Applications, vol 29. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8895-0_4

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  • DOI: https://doi.org/10.1007/978-3-0348-8895-0_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9818-8

  • Online ISBN: 978-3-0348-8895-0

  • eBook Packages: Springer Book Archive

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