User sylvester-h - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T12:23:53Z http://mathoverflow.net/feeds/user/30731 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/119199/norm-of-differential-operator-between-sobolev-spaces Norm of differential operator between Sobolev spaces Sylvester-H 2013-01-17T17:31:06Z 2013-01-20T08:38:37Z <p>It is easy to check that the differential operator $\partial^a$ (where $\alpha\in \mathbb{N}_0^n$) is continuous between the Sobolev spaces (with usual norms) $W^{m,p}(U)\to W^{m-|\alpha|,p}(U)$, where $p\in [1,+\infty]$, and $U$ is an open subset of $\mathbb{R}^n$.</p> <p>My question is : do we know exactly the value of the norm of such (bounded) operator (in this generality, or with conditions on $U$ or the other parameters). (At least this norm is less than one, it is equal to one ?). </p>