Estimates for the $${\bar{\partial }}$$-Equation on Canonical Surfaces
| Autor: | Richard Lärkäng, Mats Andersson, Jean Ruppenthal, Elizabeth Wulcan, Håkan Samuelsson Kalm |
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| Rok vydání: | 2019 |
| Předmět: |
Surface (mathematics)
Pure mathematics Mathematics - Complex Variables Bar (music) High Energy Physics::Phenomenology 010102 general mathematics Cauchy–Riemann equations 01 natural sciences Canonical singularity symbols.namesake Singularity Differential geometry Fourier analysis 0103 physical sciences FOS: Mathematics symbols High Energy Physics::Experiment 010307 mathematical physics Geometry and Topology Boundary value problem Complex Variables (math.CV) 0101 mathematics Mathematics |
| Zdroj: | The Journal of Geometric Analysis. 30:2974-3001 |
| ISSN: | 1559-002X 1050-6926 |
| 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. 21 pages |
| Databáze: | OpenAIRE |
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