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A trace theorem for solutions of linear partial differential equations

✍ Scribed by Gang Bao; William W. Symes

Publisher: John Wiley and Sons
Year: 1991
Tongue: English
Weight: 474 KB
Volume: 14
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670140803

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✦ Synopsis

Abstract

In this paper, we prove a trace regularity theorem for the solutions of general linear partial differential equations with smooth coefficients. Our result shows that by imposing additional microlocal smoothness along certain directions, the trace of the solution on a codimension‐one hypersuface will be just as regular as the solution itself. The proof is based on the Hörmander–Nirenberg pseudo‐differential cut‐off technique and a ‘fattening’ lemma, together with standard energy estimates.

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