论文标题
抛物线竖琴不平等的稳定性在度量空间上
Stability of parabolic Harnack inequalities on metric measure spaces
论文作者
论文摘要
令$（x，d，μ）$为具有局部常规Dirichlet形式的公制度量空间。我们为抛物线不平等的抛物线不平等提供了必要和充分的条件，并提供全球时空规模指数$β\ ge 2 $。我们表明，这种抛物线harnack不平等在粗糙的异构体下是稳定的。结果，一旦在公制的测量空间上确定了这样的harnack不等式，它就可以在空间的图近似中自然定义的歧管上以差异形式的任何均匀的椭圆形算子。
Let $(X,d,μ)$ be a metric measure space with a local regular Dirichlet form. We give necessary and sufficient conditions for a parabolic Harnack inequality with global space-time scaling exponent $β\ge 2$ to hold. We show that this parabolic Harnack inequality is stable under rough isometries. As a consequence, once such a Harnack inequality is established on a metric measure space, then it holds for any uniformly elliptic operator in divergence form on a manifold naturally defined from the graph approximation of the space.
