Exact sequences and estimates for the ∂¯ -problem

Debraj Chakrabarti; Phillip S. Harrington

doi:10.1007/s00209-021-02750-6

Exact sequences and estimates for the ∂¯ -problem

Debraj Chakrabarti, Phillip S. Harrington

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study Sobolev estimates for solutions of the inhomogenous Cauchy–Riemann equations on annuli in Cⁿ, by constructing exact sequences relating the Dolbeault cohomology of the annulus with respect to Sobolev spaces of forms with those of the envelope and the hole. We also obtain solutions with prescribed support and estimates in Sobolev spaces using our method.

Original language	English
Pages (from-to)	1837-1873
Number of pages	37
Journal	Mathematische Zeitschrift
Volume	299
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-021-02750-6
State	Published - Dec 2021

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abstract = "We study Sobolev estimates for solutions of the inhomogenous Cauchy–Riemann equations on annuli in Cn, by constructing exact sequences relating the Dolbeault cohomology of the annulus with respect to Sobolev spaces of forms with those of the envelope and the hole. We also obtain solutions with prescribed support and estimates in Sobolev spaces using our method.",

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N2 - We study Sobolev estimates for solutions of the inhomogenous Cauchy–Riemann equations on annuli in Cn, by constructing exact sequences relating the Dolbeault cohomology of the annulus with respect to Sobolev spaces of forms with those of the envelope and the hole. We also obtain solutions with prescribed support and estimates in Sobolev spaces using our method.

AB - We study Sobolev estimates for solutions of the inhomogenous Cauchy–Riemann equations on annuli in Cn, by constructing exact sequences relating the Dolbeault cohomology of the annulus with respect to Sobolev spaces of forms with those of the envelope and the hole. We also obtain solutions with prescribed support and estimates in Sobolev spaces using our method.

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SP - 1837

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ER -

Exact sequences and estimates for the ∂¯ -problem

Abstract

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