论文标题
全局Lorentz的Quasilarear方程梯度估计，具有强烈奇异的情况的测量数据：$ 1 <p \ leq \ frac {3n-2} {2n-1} $
Global Lorentz gradient estimates for quasilinear equations with measure data for the strongly singular case: $1<p\leq \frac{3n-2}{2n-1}$
论文作者
论文摘要
在本文中，我们研究洛伦兹空间中的全球规律性估计值，以置于\ begin的测量数据{eqnarray*} \ left \ left \ oken {array} {array} {rcl} {rcl} {rm rm {\ rm div}（\ rm div}（\ rm div}（\ rm div}）） \ text {in} 〜Ω，u＆=＆0 \ quad \ text {on}〜\partialΩ，\ end end {array} \ right。 \ end {eqnarray*}其中，$μ$是$ω$，$ω\ subset \ mathbb {r}^n $的有限尺寸，是一个有界域，使其补充$ \ mathbb {r}^n \backslashΩ$ p $ p $ p $ p $ \ rate and $ \ mather}有价值的功能满足强度奇异的情况的增长和单调性条件$ 1 <p \ leq \ frac {3n-2} {2n-1} $。我们的结果将较早的结果\ cite {55ph0，tran19}扩展到了强烈的奇异案例$ 1 <p \ leq \ frac {3n-2} {2n-1} $，以及最近的结果\ cite {hp}，通过考虑域上的粗糙条件{hp}，通过对域$ω$和非linearearity $ω$ $ \ nrineareality $ \ nraneareity $ \ m nathcal} $ {a}。
In this paper, we study the global regularity estimates in Lorentz spaces for gradients of solutions to quasilinear elliptic equations with measure data of the form \begin{eqnarray*} \left\{ \begin{array}{rcl} -{\rm div}(\mathcal{A}(x, \nabla u))&=& μ\quad \text{in} ~Ω, u&=&0 \quad \text{on}~ \partial Ω, \end{array}\right. \end{eqnarray*} where $μ$ is a finite signed Radon measure in $Ω$, $Ω\subset \mathbb{R}^n$ is a bounded domain such that its complement $\mathbb{R}^n\backslashΩ$ is uniformly $p$-thick and $\mathcal{A}$ is a Carathéodory vector valued function satisfying growth and monotonicity conditions for the strongly singular case $1<p\leq \frac{3n-2}{2n-1}$. Our result extends the earlier results \cite{55Ph0,Tran19} to the strongly singular case $1<p\leq \frac{3n-2}{2n-1}$ and a recent result \cite{HP} by considering rough conditions on the domain $Ω$ and the nonlinearity $\mathcal{A}$.
