Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces☆
Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces☆
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DOI：
10.1016/s0022-1236(02)00090-3
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发表时间：
2003-08
影响因子：
1.7
通讯作者：
P. Koskela;Kai Rajala;N. Shanmugalingam
中科院分区：
文献类型：
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作者：
P. Koskela;Kai Rajala;N. Shanmugalingam
利用热方程在一定的度量空间中建立了Cheeger调和函数的Lipschitz连续性。所考虑的度量空间是那些被赋予支持（1，2）-Poincaré不等式的加倍测度的度量空间，并且还支持相应的Sobolev-Poincaré型不等式，用于修改通过热核获得的测度。最后举例说明了我们在这些空间上所作假设的必要性。我们还提供了一个例子来表明，在一般设置的最佳可能的正则性的Cheeger调和函数是Lipschitz连续性。
We use the heat equation to establish the Lipschitz continuity of Cheeger-harmonic functions in certain metric spaces. The metric spaces under consideration are those that are endowed with a doubling measure supporting a (1,2)-Poincaré inequality and in addition supporting a corresponding Sobolev–Poincaré-type inequality for the modification of the measure obtained via the heat kernel. Examples are given to illustrate the necessity of our assumptions on these spaces. We also provide an example to show that in the general setting the best possible regularity for the Cheeger-harmonic functions is Lipschitz continuity.