论文标题
提高了$ p $ poisson方程的规律性
Improved regularity for the $p$-Poisson equation
论文作者
论文摘要
在本文中，我们为$ p $ poisson方程的解决方案产生了新的，最佳的规律性结果。我们通过一种微妙的近似方法来争论指数$ p $的微小态度，该方法从Laplace操作员驱动的限制配置文件中导入信息。我们的论点包含了技术兴趣的新颖性，即顺序稳定性的结果；它将解决方案与谐波功能连接到$ p $ - 波森方程式，从而改善了前者的规律性。我们的发现将小型制度与改进的$ \ MATHCAL {C}^{1,1 - } $ - 估计在$ l^\ infty $ -source条款的情况下进行估计。
In this paper we produce new, optimal, regularity results for the solutions to $p$-Poisson equations. We argue through a delicate approximation method, under a smallness regime for the exponent $p$, that imports information from a limiting profile driven by the Laplace operator. Our arguments contain a novelty of technical interest, namely a sequential stability result; it connects the solutions to $p$-Poisson equations with harmonic functions, yielding improved regularity for the former. Our findings relate a smallness regime with improved $\mathcal{C}^{1,1-}$-estimates in the presence of $L^\infty$-source terms.
