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2022, Volume 15, Issue 4: 535-550. Doi: 10.3934/krm.2021037
This issue Previous Article Instantaneous smoothing and exponential decay of solutions for a degenerate evolution equation with application to Boltzmann's equation Next Article Lagrangian dual framework for conservative neural network solutions of kinetic equations

Pointwise bounds for the Green's function for the Neumann-Laplace operator in $ \text{R}^3 $

  • Indiana University, Department of Mathematics, Bloomington, IN, USA

Bob Glassey and I often discussed the pedagogy of applied analysis, agreeing in particular that elementary facts should have elementary proofs. This work is offered in that spirit and in his memory

Received:  June 2021
Revised:  October 2021
Early access:  November 2021
Published:  August 2022
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    Abstract

  • We derive pointwise bounds for the Green's function and its derivatives for the Laplace operator on smooth bounded sets in $ {\bf R}^3 $ subject to Neumann boundary conditions. The proofs require only ordinary calculus, scaling arguments and the most basic facts of $ L^2 $-Sobolev space theory.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:
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