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Green Function Estimates Lead to Neumann Function Estimates

  • Guido Sweers
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 161)

Abstract

It is shown that the Neumann function for −Δu+u=f on a bounded domain Ω⊂ℝ n can be estimated pointwise from below in a uniform way. The proof is based on known uniform estimates from below for the Green function.

Keywords

Neumann function Fundamental solution Comparison principle 

Mathematics Subject Classification

35J25 35B51 35J08 

Notes

Acknowledgements

This note would not have been written, if Pavol Quittner had not been asking the right questions. I thank him for the inspiration. I also thank the referee for his comments which thoroughly simplified the proof.

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnCologneGermany

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