Counting Function Asymptotics and the Weak Weyl-Berry Conjecture for Connected Domains with Fractal Boundaries

In this paper,we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture.We prove,for some special connected fractal domains,the sharp estimate for second term of counting function asymptotics,which implies that the weak form of the Weyl- Berry conjecture holds for the case.Finally,we also study a naturally connected fractal domain,and we prove,in this case,the weak Weyl-Berry conjecture holds as well.

混合边值条件下Laplace方程的等谱问题以及分形鼓(英文)

本文将首先在R2 和R3 中各自构造出一对混合边值条件的等谱非等距同构的基本构件 ,并且在R2 中利用自相似的方法构造出相应的等谱非等距同构分形鼓 .在此基础上 ,本文讨论了这类分形鼓的波数目函数的渐近估计 。