Balayage of measures: behavior near a corner
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914337045610496 |
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| author | Charlier, Christophe Lenells, Jonatan |
| author_facet | Charlier, Christophe Lenells, Jonatan |
| contents | We consider the balayage of a measure $μ$ defined on a domain $Ω$ onto its boundary $\partial Ω$. Assuming that $Ω$ has a corner of opening $πα$ at a point $z_0 \in \partial Ω$ for some $0 < α\leq 2$ and that $dμ(z) \asymp |z-z_{0}|^{2b-2}d^{2}z$ as $z\to z_0$ for some $b > 0$, we obtain the precise rate of vanishing of the balayage of $μ$ near $z_{0}$. The rate of vanishing is universal in the sense that it only depends on $α$ and $b$. We also treat the case when the domain has multiple corners at the same point. Moreover, when $2b\leq \frac{1}α$, we provide explicit constants for the upper and lower bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Balayage of measures: behavior near a corner Charlier, Christophe Lenells, Jonatan Classical Analysis and ODEs We consider the balayage of a measure $μ$ defined on a domain $Ω$ onto its boundary $\partial Ω$. Assuming that $Ω$ has a corner of opening $πα$ at a point $z_0 \in \partial Ω$ for some $0 < α\leq 2$ and that $dμ(z) \asymp |z-z_{0}|^{2b-2}d^{2}z$ as $z\to z_0$ for some $b > 0$, we obtain the precise rate of vanishing of the balayage of $μ$ near $z_{0}$. The rate of vanishing is universal in the sense that it only depends on $α$ and $b$. We also treat the case when the domain has multiple corners at the same point. Moreover, when $2b\leq \frac{1}α$, we provide explicit constants for the upper and lower bounds. |
| title | Balayage of measures: behavior near a corner |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2403.02964 |