Abstract
The strong maximum principle of E. Hopf says that a solution of an elliptic PDE cannot assume an interior maximum. This leads to further results about solutions of such PDEs, like removability of singularities, gradient bounds, or Liouville’s theorem saying that every bounded harmonic functions defined on all of Euclidean space is constant.
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© 2003 Springer-Verlag Berlin Heidelberg
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Jost, J. (2003). The Maximum Principle. In: Postmodern Analysis. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05306-5_25
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DOI: https://doi.org/10.1007/978-3-662-05306-5_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43873-1
Online ISBN: 978-3-662-05306-5
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