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Questions about linear partial differential equations. Often used in combination with the top-level tag ap.analysis-of-pdes.
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Does hypoellipticity imply the existence of a parametrix?
Let $M$ be a smooth manifold, like $\mathbb{R}^n$ for instance. The existence of a parametrix for an operator $P$ on $C^\infty(M)$ in any reasonable pseudodifferential calculus implies that $P$ is hy …