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Accession Number:
AD0701718
Title:
NONEXISTENCE OF A CONTINUOUS RIGHT INVERSE FOR SURJECTIVE LINEAR PARTIAL DIFFERENTIAL OPERATIONS WITH CONSTANT COEFFICIENTS.
Corporate Author:
WISCONSIN UNIV MADISON
Report Date:
1970-01-01
Abstract:
Let PD denote a linear partial differential operator with constant coefficients of positive degree. Let VP denote the vector space spanned by the characteristics of PD and let dim VP denote its dimension. Suppose PD has n or 2 independent variables. In earlier work the author showed that if dim VP or n - 2, then PD has no continuous right inverse in C superscript infinity symbol Omega for any open subset Omega of R superscript n. Under suitable nonhyperbolicity hypothesis if dim VP n - 1, then PD has no continuous right inverse. These nonexistence results are extended in this paper to the case where dim VP n, but Omega is required to satisfy additional hypothesis. More precisely, Omega must contain a truncated cone V with an axis of symmetry along a nonhyperbolic direction, whose vertex touches the boundary of Omega, and which satisfies the additional hypothesis that every characteristic hyperplane which meets the vertex meets the base. Author
Descriptive Note:
Technical rept.,
Pages:
0049
Contract Number:
N00014-67-A-0128-0014
File Size:
0.00MB
