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arXiv · 2406.15153

Cancellation Properties and Pointwise Bounds for the Green's Functions for the Laplace Operator

David Hoff
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Abstract

We derive a cancellation property satisfied by the derivatives of the Green's functions for the Laplace operator corresponding to Dirichlet and Neumann boundary conditions on bounded sets in $\R^n$. The main result is derived in a broader, self-contained exposition which includes construction of and basic pointwise bounds for the Green's functions and their derivatives. We also give an application of the cancellation property to a problem in fluid mechanics.

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David Hoff. 2024-06-21. Cancellation Properties and Pointwise Bounds for the Green's Functions for the Laplace Operator. https://arxiv.org/abs/2406.15153

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