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A trace theorem for solutions of linear partial differential equations
Author(s) -
Bao Gang,
Symes William W.
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140803
Subject(s) - mathematics , trace (psycholinguistics) , smoothness , lemma (botany) , mathematical analysis , partial differential equation , parabolic partial differential equation , codimension , pure mathematics , ecology , philosophy , linguistics , poaceae , biology
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.