Abstract
LetP be a differential operator with constant coefficients in ℝ n . Ifu is a distribution, the singular support ofu is the complement of the largest set whereu ∈C ∞. Necessary and sufficient conditinos are obtained for a closed convex set Γ to be equal to the singular support ofu for someu withPu ∈C ∞ or, equivalently, for Γ to contain the singular support ofu for someu withPu ∈C ∞ butu ∉C ∞. Related local uniqueness theorems analogous to the Holmgren theorem with supports replaced by singular supports are also given, as well as applications concerningP-convexity with respect to singular supports.
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