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A remark on a compactness result in electromagnetic theory

✍ Scribed by Karl J. Witsch

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 281 KB
Volume: 16
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670160205

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✦ Synopsis

Abstract

Calderon's extension theorem is a crucial tool in the proof of the compactneσs of the resolvent for the Maxwell operator, and whence this result is proved for domains with the strict cone property. However, the proof only requires an extension operator that extends W^2,2^‐functions compactly as W^1,2^‐functions. It is shown that this can be achieved under weaker regularity conditions on the domain: the cone may be replaced by some cusp of an appropriate order.

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