The Leibniz rule for the Dirichlet and the Neumann Laplacian

Tsukasa Iwabuchi

The Leibniz rule for the Dirichlet and the Neumann Laplacian

Analysis of PDEs 2019-11-27 v2

Authors: Tsukasa Iwabuchi

Abstract

We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half space case, which is related to not only smoothness of functions and but also boundary behavior. The crucial point for the proof is how to handle boundary values of functions and their derivatives.

Keywords

leibniz rule dirichlet laplacian neumann laplacian sobolev spaces bilinear estimates boundary value half space

Cite

@article{arxiv.1905.02854,
  title  = {The Leibniz rule for the Dirichlet and the Neumann Laplacian},
  author = {Tsukasa Iwabuchi},
  journal= {arXiv preprint arXiv:1905.02854},
  year   = {2019}
}

Comments

19 pages

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