截断函数的能量不等式及其应用
Energy inequalities for cutoff functions and some applications
摘要：
考虑具有局部正则Dirichlet型的度量测度空间.建立了次扩散时空指数下热核上界成立的充要条件。这个特征在粗糙等距下是稳定的，也就是说，它在狄利克雷形式的有界扰动下保持不变。此外，我们给出了随机完备性的一个标准的Sobolev不等式的截断函数。作为一个例子，我们表明，这个标准适用于测地线不完整的分形空间上的异常扩散，在体积增长方面的既定标准失败。
英文摘要：
We consider a metric measure space with a local regular Dirichlet form. We establish necessary and sufficient conditions for upper heat kernel bounds with sub-diffusive space-time exponent to hold. This characterization is stable under rough isometries, that is it is preserved under bounded perturbations of the Dirichlet form. Further, we give a criterion for stochastic completeness in terms of a Sobolev inequality for cutoff functions. As an example we show that this criterion applies to an anomalous diffusion on a geodesically incomplete fractal space, where the well-established criterion in terms of volume growth fails.
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