论文标题
边界椭圆度和限制$ l^1 $ - 估计半空间
Boundary ellipticity and limiting $L^1$-estimates on halfspaces
论文作者
论文摘要
我们确定$ k $ th订单差异操作员的必要条件 $$ \ | d^{k-1} u \ | _ {\ Mathrm {\ Mathrm {l}^{\ frac {n} {n} {n-1}}}（h^+）} \ leq c \ | \ | \ | \ Mathbb {a} a} a} } u \ in \ mathrm {c}^\ infty_c（\ mathbb {r}^{n}，v） $$ 持有。这是由于$ h = \ partial h^+$上尖锐的跟踪定理的结果。
We identify necessary and sufficient conditions on $k$th order differential operators $\mathbb{A}$ in terms of a fixed halfspace $H^+\subset\mathbb{R}^n$ such that the Gagliardo--Nirenberg--Sobolev inequality $$ \|D^{k-1}u\|_{\mathrm{L}^{\frac{n}{n-1}}(H^+)}\leq c\|\mathbb{A} u\|_{\mathrm{L}^1(H^+)}\quad\text{for }u\in\mathrm{C}^\infty_c (\mathbb{R}^{n},V) $$ holds. This comes as a consequence of sharp trace theorems on $H=\partial H^+$.
