Estimates for the $\bar{\partial}$-equation on canonical surfaces
| Autor: | Andersson, Mats, Lärkäng, Richard, Ruppenthal, Jean, Kalm, Håkan Samuelsson, Wulcan, Elizabeth |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | J. Geom. Anal. 30 (2020), no. 3, 2974-3001 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s12220-019-00187-2 |
| Popis: | We study the solvability in $L^p$ of the $\bar\partial$-equation in a neighborhood of a canonical singularity on a complex surface, a so-called du Val singularity. We get a quite complete picture in case $p=2$ for two natural closed extensions $\bar\partial_s$ and $\bar\partial_w$ of $\bar\partial$. For $\bar\partial_s$ we have solvability, whereas for $\bar\partial_w$ there is solvability if and only if a certain boundary condition $(*)$ is fulfilled at the singularity. Our main tool is certain integral operators for solving $\bar\partial$ introduced by the first and fourth author, and we study mapping properties of these operators at the singularity. Comment: 21 pages |
| Databáze: | arXiv |
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