论文标题
$ l^p $估算具有混合边界条件的椭圆系统的平方根ii
$L^p$-estimates for the square root of elliptic systems with mixed boundary conditions II
论文作者
论文摘要
我们显示了$ l^p $估计的二阶二阶复杂椭圆系统的平方根$ l $在$ \ mathbb {r}^d $中的开放集上的差异形式。基础集应该是在诺伊曼边界部分附近的局部统一，而dirichlet边界部分是ahlfors-david的常规。可用的估计值的间隔的下端值是由$ -L $生成的半群的$ p $结合性属性，以及通过宽敞的同构的外推属性的上端点。另外，我们表明外推范围相对以$（1，\ infty）$开放。
We show $L^p$ estimates for square roots of second order complex elliptic systems $L$ in divergence form on open sets in $\mathbb{R}^d$ subject to mixed boundary conditions. The underlying set is supposed to be locally uniform near the Neumann boundary part, and the Dirichlet boundary part is Ahlfors-David regular. The lower endpoint for the interval where such estimates are available is characterized by $p$-boundedness properties of the semigroup generated by $-L$, and the upper endpoint by extrapolation properties of the Lax-Milgram isomorphism. Also, we show that the extrapolation range is relatively open in $(1,\infty)$.
