论文标题
美元
$L^{p}$ and $\mathcal{H}^{p}_{FIO}$ regularity for wave equations with rough coefficients
论文作者
论文摘要
我们考虑具有与时间无关系数的波动方程，这些系数在空间中具有$ c^{1,1} $。我们表明，对于$ p $和$ s $的非繁琐范围，波动方程的标准不均匀初始值问题在sobolev spaces $ \ mathcal {h}^s，p}，p} _ {fio} _ {fio}（\ mathbb {\ mathb {r}^n}^{r}^{n}）$上$ \ MATHCAL {h}^{p} _ {fio}（\ Mathbb {r}^{n}）$ for smith的作品，最近由作者和门户网站引入了最近引入的傅立叶积分运算符。在空间尺寸中，$ n = 2 $和$ n = 3 $，其中包括$ 1 <p <\ infty $。作为推论，我们为此方程式获得了最佳的固定时间$ l^{p} $规则性，在平滑系数的情况下，概括了Seeger，Sogge和Stein的工作。
We consider wave equations with time-independent coefficients that have $C^{1,1}$ regularity in space. We show that, for nontrivial ranges of $p$ and $s$, the standard inhomogeneous initial value problem for the wave equation is well posed in Sobolev spaces $\mathcal{H}^{s,p}_{FIO}(\mathbb{R}^{n})$ over the Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for Fourier integral operators introduced recently by the authors and Portal, following work of Smith. In spatial dimensions $n = 2$ and $n=3$, this includes the full range $1 < p < \infty$. As a corollary, we obtain the optimal fixed-time $L^{p}$ regularity for such equations, generalizing work of Seeger, Sogge and Stein in the case of smooth coefficients.
