论文标题
渐近平均值谐波函数在双倍度量空间中
Asymptotically mean value harmonic functions in doubling metric measure spaces
论文作者
论文摘要
我们考虑具有渐近平均值特性的函数，已知在Riemannian歧管中表征谐波，在双倍度量空间中。我们表明，对于低于一个指数的任何指数，强烈的AMV谐波函数都是连续的。更笼统地，我们用有限的AMV-norm定义了功能类别，并表明该类别的函数属于分数Hajlasz-Sobolev空间，它们的爆炸使均值属性满足。此外，在加权的欧几里得环境中，我们发现AMV谐波功能满足椭圆形PDE。
We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds, in doubling metric measure spaces. We show that the strongly amv-harmonic functions are Hölder continuous for any exponent below one. More generally, we define the class of functions with finite amv-norm and show that functions in this class belong to a fractional Hajlasz-Sobolev space and their blow-ups satisfy the mean-value property. Furthermore, in the weighted Euclidean setting we find an elliptic PDE satisfied by amv-harmonic functions.
