Characterization of ellipticity for linear differential operators
$begingroup$
Let $P(D)$ be a differential operator of order $m$. I would like to show that $P(D)$ is elliptic if for some open and bounded subset of $mathbb{R}^n$ and for some real $s$ and $c>0$
and all $varphiin mathscr{D}(Omega)$:
$$|varphi|_{s+m}leq c|P(D)varphi|_s.$$
Many thanks in advance for your help.
pde elliptic-operators
edited Dec 17 '18 at 20:47
Daniele Tampieri
2,3972922
asked Dec 17 '18 at 19:53
Emy Emy
111
$endgroup$
add a comment |
$begingroup$
Let $P(D)$ be a differential operator of order $m$. I would like to show that $P(D)$ is elliptic if for some open and bounded subset of $mathbb{R}^n$ and for some real $s$ and $c>0$
and all $varphiin mathscr{D}(Omega)$:
$$|varphi|_{s+m}leq c|P(D)varphi|_s.$$
Many thanks in advance for your help.
pde elliptic-operators
edited Dec 17 '18 at 20:47
Daniele Tampieri
2,3972922
asked Dec 17 '18 at 19:53
Emy Emy
111
$endgroup$
add a comment |
$begingroup$
Let $P(D)$ be a differential operator of order $m$. I would like to show that $P(D)$ is elliptic if for some open and bounded subset of $mathbb{R}^n$ and for some real $s$ and $c>0$
and all $varphiin mathscr{D}(Omega)$:
$$|varphi|_{s+m}leq c|P(D)varphi|_s.$$
Many thanks in advance for your help.
pde elliptic-operators
edited Dec 17 '18 at 20:47
Daniele Tampieri
2,3972922
asked Dec 17 '18 at 19:53
Emy Emy
111
$endgroup$
Let $P(D)$ be a differential operator of order $m$. I would like to show that $P(D)$ is elliptic if for some open and bounded subset of $mathbb{R}^n$ and for some real $s$ and $c>0$
and all $varphiin mathscr{D}(Omega)$:
$$|varphi|_{s+m}leq c|P(D)varphi|_s.$$
Many thanks in advance for your help.
pde elliptic-operators
pde elliptic-operators
edited Dec 17 '18 at 20:47
Daniele Tampieri
2,3972922
asked Dec 17 '18 at 19:53
Emy Emy
111
edited Dec 17 '18 at 20:47
Daniele Tampieri
2,3972922
asked Dec 17 '18 at 19:53
Emy Emy
111
edited Dec 17 '18 at 20:47
Daniele Tampieri
2,3972922
edited Dec 17 '18 at 20:47
Daniele Tampieri
2,3972922
edited Dec 17 '18 at 20:47
Daniele Tampieri
2,3972922
2,3972922
asked Dec 17 '18 at 19:53
Emy Emy
111
asked Dec 17 '18 at 19:53
Emy Emy
111
asked Dec 17 '18 at 19:53
Emy Emy
111
111
add a comment |
add a comment |
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