论文标题
带有测量数据的准方程的存在和规律性估计：$ 1 <p \ leq \ frac {3n-2} {2n-1} $
Existence and regularity estimates for quasilinear equations with measure data: the case $1<p\leq \frac{3n-2}{2n-1}$
论文作者
论文摘要
我们获得了与测量数据的拟议梯度梯度的存在和全球规则性估计，其原型的原型为$ - {\ rm div}（| \ nabla u |^{p-2} {p-2} \ nabla U =δ非平滑边界。 $δ= 0 $或$δ= 1 $，$μ$是$ω$的有限签名ra量，$ q $是线性或超级线性增长，即$ q \ geq 1 $。我们的主要关注点是将早期结果扩展到强烈的奇数案例$ 1 <p \ leq \ frac {3n-2} {2n-1} $。特别是，在与Riccati类型方程相对应的情况下，我们解决了文献中已经提出了一段时间的解决性问题。
We obtain existence and global regularity estimates for gradients of solutions to quasilinear elliptic equations with measure data whose prototypes are of the form $-{\rm div} (|\nabla u|^{p-2} \nabla u)= δ\, |\nabla u|^q +μ$ in a bounded main $\Om\subset\RR^n$ potentially with non-smooth boundary. Here either $δ=0$ or $δ=1$, $μ$ is a finite signed Radon measure in $Ω$, and $q$ is of linear or super-linear growth, i.e., $q\geq 1$. Our main concern is to extend earlier results to the strongly singular case $1<p\leq \frac{3n-2}{2n-1}$. In particular, in the case $δ=1$ which corresponds to a Riccati type equation, we settle the question of solvability that has been raised for some time in the literature.
