Lipschitz度量谱簇的次临界Lp界
Subcritical Lp bounds on spectral clusters for Lipschitz metrics
摘要：
在二维Dirichlet型的Lipschitz正则性系数的情况下，我们建立了谱局部化函数L^p范数的渐近界。这些界限对于p>6的范围是新的。证明中的一个关键步骤是限制具有Lipschitz系数的双曲型方程解的能量传播速率。
英文摘要：
We establish asymptotic bounds on the L^p norms of spectrally localized functions in the case of two-dimensional Dirichlet forms with coefficients of Lipschitz regularity. These bounds are new for the range p>6. A key step in the proof is bounding the rate at which energy spreads for solutions to hyperbolic equations with Lipschitz coefficients.
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