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# Principal part of elliptic differential operator.

2017-12-03 03:08:21

I have an elliptic differential operator in ${\mathbb{R}}^n$, of order $m$ and constant coefficients.

How can I show that if the principal part of $P$ is $P_m(k) = {a}_{\alpha}k^{\alpha}$, then for all $k\in {\mathbb{R}}^n$ there exist a constant $c >0$ such that $|P_m(k)| \geq c |k|^m$?