Exact sequences and estimates for the ∂¯ -problem

Debraj Chakrabarti, Phillip S. Harrington

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1837-1873
Number of pages37
JournalMathematische Zeitschrift
Issue number3-4
StatePublished - Dec 2021


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