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The Maximum Principle, Elliptic Regularity, and Applications

  • Hervé Le Dret
Chapter
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Part of the Universitext book series (UTX)

Abstract

The expression “maximum principle” is a generic term that covers a set of results of two kinds. One kind concerns the points of maximum or minimum of solutions of certain boundary value problems, elliptic in our case. The other kind is about monotone dependence of the solutions with respect to the data. The two aspects are naturally related to one another. There are furthermore two general contexts, the so-called “strong” context in which classical solutions are considered, and the “weak” context in which variational solutions are considered. This terminology is not universal however.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hervé Le Dret
    • 1
  1. 1.Laboratoire Jacques-Louis LionsSorbonne UniversitéParisFrance

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