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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2403.19341 |
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| _version_ | 1866929623220092928 |
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| author | Carletti, Lorenzo |
| author_facet | Carletti, Lorenzo |
| contents | We show existence, uniqueness and positivity for the Green's function of the operator $(Δ_g + α)^k$ in a closed Riemannian manifold $(M,g)$, of dimension $n>2k$, $k\in \mathbb{N}$, $k\geq 1$, with Laplace-Beltrami operator $Δ_g = -\operatorname{div}_g(\nabla \cdot)$, and where $α>0$. We are interested in the case where $α$ is large : We prove pointwise estimates with explicit dependence on $α$ for the Green's function and its derivatives. We highlight a region of exponential decay for the Green's function away from the diagonal, for large $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Green's function of polyharmonic operators with diverging coefficients: Construction and sharp asymptotics Carletti, Lorenzo Analysis of PDEs 35J08, 35J30, 35C15, 58J05, 35C20, We show existence, uniqueness and positivity for the Green's function of the operator $(Δ_g + α)^k$ in a closed Riemannian manifold $(M,g)$, of dimension $n>2k$, $k\in \mathbb{N}$, $k\geq 1$, with Laplace-Beltrami operator $Δ_g = -\operatorname{div}_g(\nabla \cdot)$, and where $α>0$. We are interested in the case where $α$ is large : We prove pointwise estimates with explicit dependence on $α$ for the Green's function and its derivatives. We highlight a region of exponential decay for the Green's function away from the diagonal, for large $α$. |
| title | The Green's function of polyharmonic operators with diverging coefficients: Construction and sharp asymptotics |
| topic | Analysis of PDEs 35J08, 35J30, 35C15, 58J05, 35C20, |
| url | https://arxiv.org/abs/2403.19341 |