Discrete approximations to Dirichlet and Neumann Laplacians on a half-space and norm resolvent convergence

Horia Cornean, Henrik Garde, Arne Jensen

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Abstract

We extend recent results on discrete approximations of the Laplacian in Rd with norm resolvent convergence to the corresponding results for Dirichlet and Neumann Laplacians on a half-space. The resolvents of the discrete Dirichlet/Neumann Laplacians are embedded into the continuum using natural discretization and embedding operators. Norm resolvent convergence to their continuous counterparts is proven with a quadratic rate in the mesh size. These results generalize with a limited rate to also include operators with a real, bounded, and Hölder continuous potential, as well as certain functions of the Dirichlet/Neumann Laplacians, including any positive real power.

OriginalsprogEngelsk
TidsskriftStudia Mathematica
Vol/bind271
Sider (fra-til)225-236
Antal sider12
ISSN0039-3223
DOI
StatusUdgivet - 2023

Bibliografisk note

Funding Information:
Acknowledgements. This research is partially supported by grant 8021–00084B from the Independent Research Fund Denmark, Natural Sciences.

Publisher Copyright:
© Instytut Matematyczny PAN, 2023.

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