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Global boundary regularity for the -equation on q-pseudoconvex domains

โœ Scribed by Heungju Ahn

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
141 KB
Volume
280
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Abstract

We introduce a notion of q โ€pseudoconvex domain of new type for a bounded domain of โ„‚^n^ and prove that for given a $ \bar \partial $โ€closed (p, r)โ€form, r โ‰ฅ q, that is smooth up to the boundary, there exists a (p, r โ€“ 1)โ€form smooth up to the boundary which is a solution of $ \bar \partial $โ€equation on a bounded q โ€pseudoconvex domain. (ยฉ 2007 WILEYโ€VCH Verlag GmbH & Co. KGaA, Weinheim)

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Asymptotic and exact local radiation boundary conditions (RBC) for the scalar time-dependent wave equation, รฟrst derived by Hagstrom and Hariharan, are reformulated as an auxiliary Cauchy problem for each radial harmonic on a spherical boundary. The reformulation is based on the hierarchy of local b