Moser iteration for (quasi)minimizers on metric spaces
Moser iteration for (quasi)minimizers on metric spaces
复制标题
度量空间上（拟）极小化器的 Moser 迭代
DOI：
10.1007/s00229-006-0040-8
复制
发表时间：
2006
影响因子：
0.6
通讯作者：
N. Marola
中科院分区：
文献类型：
--
作者：
Anders Björn;N. Marola
研究了度量测度空间上p-Dirichlet积分拟极小的正则性。我们适应这种设置的Moser迭代技术，并表明它可以应用于没有一个基本的微分方程。然而，我们已经能够运行的Moser迭代完全只有极小。我们证明了Caccioppoli不等式和局部有界性的quasissub-和quasissuperminimizers。这是在度量空间中完成的，配备了加倍测度并支持弱（1，p）-Poincaré不等式。度量空间不要求是完备的。我们还提供了一个例子，证明了在Harnack不等式中球的条件下，弱Poincaré不等式中的伸缩常数是必不可少的.这一事实似乎已被忽视的早期文献中的非线性潜力理论的度量空间。
We study regularity properties of quasiminimizers of the p-Dirichlet integral on metric measure spaces. We adapt the Moser iteration technique to this setting and show that it can be applied without an underlying differential equation. However, we have been able to run the Moser iteration fully only for minimizers. We prove Caccioppoli inequalities and local boundedness properties for quasisub- and quasisuperminimizers. This is done in metric spaces equipped with a doubling measure and supporting a weak (1, p)-Poincaré inequality. The metric space is not required to be complete. We also provide an example which shows that the dilation constant from the weak Poincaré inequality is essential in the condition on the balls in the Harnack inequality. This fact seems to have been overlooked in the earlier literature on nonlinear potential theory on metric spaces.