Weyl's Law for the Steklov Problem on Surfaces with Rough Boundary

被引：3
作者：
Karpukhin, Mikhail [1 ]
Lagace, Jean [2 ]
Polterovich, Iosif [3 ]
机构：
[1] UCL, Dept Math, Gower St, London WC1E 6BT, England
[2] Kings Coll London, Dept Math, London WC2R 2LS, England
[3] Univ Montreal, Dept Math & Stat, CP 6128,Succ Ctr Ville, Montreal, PQ H3C 3J7, Canada
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2023年 / 247卷 / 05期
基金：
加拿大自然科学与工程研究理事会; 英国工程与自然科学研究理事会;
关键词：
ASYMPTOTIC-BEHAVIOR; DOMAINS; EIGENVALUES; LAPLACIAN; FORMULA;
D O I：
10.1007/s00205-023-01912-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The validity of Weyl's law for the Steklov problem on domains with Lipschitz boundary is a well-known open question in spectral geometry. We answer this question in two dimensions and show that Weyl's law holds for an even larger class of surfaces with rough boundaries. This class includes domains with interior cusps as well as "slow" exterior cusps. Moreover, the condition on the speed of exterior cusps cannot be improved, which makes our result, in a sense optimal. The proof is based on the methods of Suslina and Agranovich combined with some observations about the boundary behaviour of conformal mappings.
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页数：20
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