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Schauder estimates at the boundary for sub-laplacians in Carnot groups

  • Annalisa Baldi
  • Giovanna CittiEmail author
  • Giovanni Cupini
Article
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Abstract

In this paper we present a new approach to prove Schauder estimates at the boundary for sub-Laplacian type operators in Carnot groups. While internal Schauder estimates have been deeply studied, up to now subriemannian estimates at the boundary are known only in the Heisenberg groups. The proof of these estimates in the Heisenberg setting, due to Jerison (J Funct Anal 43:97–142, 1981), is based on the Fourier transform technique and cannot be repeated in general Lie groups. After the result of Jerison no new contribution to the boundary problem has been provided. In this paper we introduce a new method, which allows to build a Poisson kernel starting from the fundamental solution, from which we deduce the Schauder estimates at non characteristic boundary points.

Mathematics Subject Classification

35R03 35B65 35J25 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Annalisa Baldi
    • 1
  • Giovanna Citti
    • 1
    Email author
  • Giovanni Cupini
    • 1
  1. 1.Dipartimento di MatematicaBolognaItaly

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