论文标题
奇异抛物线量度数据问题的规律性估计，急剧增长
Regularity estimates for singular parabolic measure data problems with sharp growth
论文作者
论文摘要
我们证明了带有测量数据的抛物线$ p $ -laplace类型方程的全局梯度估计，其模型为$$ u_t-\ textrm {div} \ left（| | du |^{p-2} du \ right）=μ\ quad \ quad \ quad \ quad \ quad \ textrm {in} \ Mathbb {r}，$$，其中$μ$是具有有限总质量的签名ra。我们考虑奇异的情况$$ \ frac {2n} {n+1} <p \ le 2- \ frac {1} {1} {n+1} $$，并给出$ω$的非线性和边界的最小条件，这可以保证此类测量数据问题的规律性结果。
We prove global gradient estimates for parabolic $p$-Laplace type equations with measure data, whose model is $$u_t - \textrm{div} \left(|Du|^{p-2} Du\right) = μ\quad \textrm{in} \ Ω\times (0,T) \subset \mathbb{R}^n \times \mathbb{R},$$ where $μ$ is a signed Radon measure with finite total mass. We consider the singular case $$\frac{2n}{n+1} <p \le 2-\frac{1}{n+1}$$ and give possibly minimal conditions on the nonlinearity and the boundary of $Ω$, which guarantee the regularity results for such measure data problems.
