论文标题
$ p $ laplacian的本地界限，具有退化系数
Local boundedness for $p$-Laplacian with degenerate coefficients
论文作者
论文摘要
我们研究了非线性非椭圆形方程的亚物物的局部界限，其原型由$ \ nabla \ cdot（λ| \ nabla u |^{p-2} \ nabla u）= 0 $给出，其中可变系数$ 0 \leqλ$ and inverse $λ^and允许使用。假设在$λ$和$λ^{ - 1} $上的某些集成性条件取决于$ p $和尺寸，我们将显示本地边界。此外，我们为规律性提供反例，表明每$ p> 1 $的集成性条件是最佳的。
We study local boundedness for subsolutions of nonlinear nonuniformly elliptic equations whose prototype is given by $\nabla \cdot (λ|\nabla u|^{p-2}\nabla u)=0$, where the variable coefficient $0\leqλ$ and its inverse $λ^{-1}$ are allowed to be unbounded. Assuming certain integrability conditions on $λ$ and $λ^{-1}$ depending on $p$ and the dimension, we show local boundedness. Moreover, we provide counterexamples to regularity showing that the integrability conditions are optimal for every $p>1$.
