Cancellation Properties and Pointwise Bounds for the Green's Functions for the Laplace Operator
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929394279251968 |
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| author | Hoff, David |
| author_facet | Hoff, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cancellation Properties and Pointwise Bounds for the Green's Functions for the Laplace Operator Hoff, David Analysis of PDEs 35B85, 35J05, 35J08 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. |
| title | Cancellation Properties and Pointwise Bounds for the Green's Functions for the Laplace Operator |
| topic | Analysis of PDEs 35B85, 35J05, 35J08 |
| url | https://arxiv.org/abs/2406.15153 |