论文标题
高阶椭圆方程的$ l^p $ neumann问题
The $L^p$ Neumann problem for higher order elliptic equations
论文作者
论文摘要
We solve the Neumann problem in the half space $\mathbb{R}^{n+1}_+$, for higher order elliptic differential equations with variable self-adjoint $t$-independent coefficients, and with boundary data in $L^p$, where $\max\bigl(1,\frac{2n}{n+2}-\varepsilon\bigr) <p <2 $。 我们还根据$ l^p $或$ \ dot w^{\ pm1，p} $在$ l^p $或$ p $的$ l^p $或$ \ dot w^{\ pm1，$ p $的输入中建立了非义务和区域积分估计，该输入是基于$ p \ geq2 $的已知范围；在这种情况下，我们可能会放松自我婚姻的要求。
We solve the Neumann problem in the half space $\mathbb{R}^{n+1}_+$, for higher order elliptic differential equations with variable self-adjoint $t$-independent coefficients, and with boundary data in $L^p$, where $\max\bigl(1,\frac{2n}{n+2}-\varepsilon\bigr) < p < 2$. We also establish nontangential and area integral estimates on layer potentials with inputs in $L^p$ or $\dot W^{\pm1,p}$ for a similar range of~$p$, based on known bounds for $p\geq2$; in this case we may relax the requirement of self-adjointess.
