Tagged Questions
1
vote
1answer
50 views
How to establish the estimate?
I consider the inequality as follows: let $a>0,b>0$, and satisfy $$2a^2-b^2\leq C(1+a).\tag{1}$$ If we assume that $b\leq a$, then there exist a constant $C_1>0$ such that $$a\leq ...
0
votes
0answers
37 views
Strichartz estimates and operator from $L^{2}_{x}$ to $L^{6}_{x,t}$
I want to prove that the operator $T=| \nabla|^{1/6} e^{-t\partial ^{3}_{x}}\tilde{P}_{N}$ takes functions from $L^{2}_{x}$ to $L^{6}_{x,t}$. The hint is to first prove for Schwartz functions, and ...
5
votes
1answer
56 views
An estimate of $C^2$
Let $u$ be a function on a domain $\Omega\subset R^n$, and $D^2u=\left(\frac{\partial^2 u}{\partial x_i\partial x_j}\right)_{n\times n}$ be the Hessian of $u$. If $D^2u$ is positively definite and ...
