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This tag is used if a reference is needed in a paper or textbook on a specific result.

5 votes
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307 views

Reference for Hodge decomposition

Let $U$ be a bounded open subset of $\mathbb{R}^d$ with Lipschitz boundary, and $g \in L^2(U,\mathbb{R}^d)$ be a solenoidal vector field (i.e. $\nabla \cdot g = 0$). Then $g$ can be written in the for …
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2 votes
1 answer
239 views

Locality of homogeneous pseudo-differential operator

Let $P$ be a polynomial in several variables, and let $P(D)$ be the corresponding differential operator. Obviously, $P(D)$ is a local operator, in the sense that I need only to know the function $u$ i …
Elwood's user avatar
  • 562