Abstract

We find that, in the critical case \(2l= {\mathbf N} \), the eigenvalues of the problem \(\lambda(-\Delta)^{l}u=Pu\) with the singular measure \(P\) supported on a compact Lipschitz surface of an arbitrary dimension in \( {\mathbb R} ^{ {\mathbf N} }\) satisfy an asymptotic formula of the same order as in the case of an absolutely continuous measure.

中文翻译：

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临界情况下带奇异测度的加权多谐算子的特征值渐近

摘要

我们发现，在临界情况下\(2l= {\mathbf N} \)，问题\(\lambda(-\Delta)^{l}u=Pu\) 的特征值具有奇异测度\(P \)支持在\( {\mathbb R} ^{ {\mathbf N} }\) 中任意维度的紧凑 Lipschitz 表面上，满足与绝对连续测度情况相同阶的渐近公式。