The ∂¯-Neumann operator with Sobolev estimates up to a finite order. Issue 10 (2nd October 2020)

• Record Type: Journal Article
• Authors: Harrington, Phillip; Liu, Bingyuan
• Is Part Of: Communications in partial differential equations. Volume 45:Issue 10(2020)
• Page Start: 1435
• Page End: 1450
• Publication Date: 2020-10-02
• Subjects: Global regularity -- The ∂¯-Neumann problem -- Sobolev estimates; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2020.1774899
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: Let Ω ⊂ C m be a bounded pseudoconvex domain with smooth boundary. For each k ∈ N, we give a sufficient condition to estimate the ∂ ¯ -Neumann operator in the Sobolev space W k ( Ω ) . The key feature of our results is a precise formula for k in terms of the geometry of the boundary of Ω. It also shows the bound in the precise formula for Sobolev estimates of order k is comparably reciprocal of the Sobolev order k .