NONEXISTENCE OF A CONTINUOUS RIGHT INVERSE FOR SURJECTIVE LINEAR PARTIAL DIFFERENTIAL OPERATIONS WITH CONSTANT COEFFICIENTS.
Abstract
Let P(D) denote a linear partial differential operator with constant coefficients of positive degree. Let V(P) denote the vector space spanned by the characteristics of P(D) and let dim V(P) denote its dimension. Suppose P(D) has n = or > 2 independent variables. In earlier work the author showed that if dim V(P) = or < n - 2, then P(D) 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 V(P) = n - 1, then P(D) has no continuous right inverse. These nonexistence results are extended in this paper to the case where dim V(P) = 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1970
- Accession Number
- AD0701718
Entities
People
- David K. Cohoon
Organizations
- University of Wisconsin–Madison