Accession Number : AD0701718

Title :   NONEXISTENCE OF A CONTINUOUS RIGHT INVERSE FOR SURJECTIVE LINEAR PARTIAL DIFFERENTIAL OPERATIONS WITH CONSTANT COEFFICIENTS.

Descriptive Note : Technical rept.,

Corporate Author : WISCONSIN UNIV MADISON

Personal Author(s) : Cohoon,David K.

Report Date : JAN 1970

Pagination or Media Count : 49

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)

Descriptors :   (*FUNCTIONAL ANALYSIS, *OPERATORS(MATHEMATICS)), (*PARTIAL DIFFERENTIAL EQUATIONS, VECTOR SPACES), TRANSFORMATIONS(MATHEMATICS), BANACH SPACE, CONVEX SETS, TOPOLOGY

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE