拟线性测度问题的良$λ$和Muckenhoupt-Wheeden型界及其应用
Good-$λ$ and Muckenhoupt-Wheeden type bounds in quasilinear measure datum problems, with applications
摘要：
利用测度数据，得到了一类拟线性椭圆型方程解的梯度的加权good- $λ$型不等式和Muckenhoupt-Wheeden型界.这样的结果是在Reifenberg意义下的$\mathbb{R}^n$中的充分平坦域上全局获得的。这里的主要运营商建模后的$p$ -拉普拉斯算子，其中第一次考虑奇异情况$\frac{3n-2}{2n-1}<p\leq 2-\frac{1}{n}$。这些界为拟线性椭圆型方程的解集提供了有用的紧性准则。作为应用，得到了一类具有线性或超线性幂增长梯度源项的拟线性Riccati型方程可去奇异集的存在性结果和可去奇异集大小的精确界.
英文摘要：
Weighted good-$λ$ type inequalities and Muckenhoupt-Wheeden type bounds are obtained for gradients of solutions to a class of quasilinear elliptic equations with measure data. Such results are obtained globally over sufficiently flat domains in $\mathbb{R}^n$ in the sense of Reifenberg. The principal operator here is modeled after the $p$-Laplacian, where for the first time singular case $\frac{3n-2}{2n-1}<p\leq 2-\frac{1}{n}$ is considered. Those bounds lead to useful compactness criteria for solution sets of quasilinear elliptic equations with measure data. As an application, sharp existence results and sharp bounds on the size of removable singular sets are deduced for a quasilinear Riccati type equation having a gradient source term with linear or super-linear power growth.
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