If $u(t,x)\in L^{2}([0,T],H^{2}(\mathbb{R}^{n}))$, $\partial_{t}u \in L^{2}([0,T],L^{2}(\mathbb{R}^{n}))$, prove that $$ u(t,x)\in C([0,T],H^{1}(\mathbb{R}^{n})) $$
Asked
Active
Viewed 57 times
1
-
Do you have a PDE that $u$ satisfies? Evans' PDE book has results of this kind. – Albert Altarovici Jan 17 '13 at 11:19
-
just to be precise, you find the theorem you are looking for on page 288 (Evans, Partial Differential Equation), theorem 4 for a general non negative integer $m$. – math Jan 17 '13 at 11:29