The Dirichlet–Neumann Paradifferential Problem

  • Massimiliano Berti
  • Jean-Marc Delort
Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 24)


The preceding chapters of this book provided a proof of our main almost global existence result for capillary-gravity wave equations, assuming that the latter have been reduced to some paradifferential system, which admits energy estimates. The goal of this chapter, and of the following ones, is to perform such a reduction. A key step is to obtain a convenient paradifferential representation of the Dirichlet–Neumann operator with a homogeneous expansion in the free wave profile at any degree. This is what we achieve in Chap. 6, constructing a paradifferential version of the Boutet de Monvel parametrix of the Dirichlet problem.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Massimiliano Berti
    • 1
  • Jean-Marc Delort
    • 2
  1. 1.Department of MathematicsInternational School for Advanced Studies SISSATriesteItaly
  2. 2.LAGASorbonne Paris-Cité/University Paris 13VilletaneuseFrance

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