Regularity at the Boundary and Tangential Regularity

2011/04/07 by Tran Vu Khanh, Khanh, Tran Vu, Giuseppe Zampieri +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #Elasticity and Wave Propagation #FOS: Mathematics #Numerical methods in inverse problems #math.CV

paper · pdf · doi:10.48550/arxiv.1104.1407

arxiv created 2011/04/07 · openalex publication_date 2011/04/07 · arxiv updated 2011/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a pseudoconvex domain in complex space, we prove the equivalence of the local hypoellipticity of the system (di-bar, di-bar*) with the system (di-bar_b,di-bar*_b) induced in the boundary. This develops a result of ours which used the theory of the "harmonic" extension by Kohn. This technique is inadequate for the purpose of the present paper and must be replaced by the "holomorphic" extension introduced by the authors in former work.

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