Neumann eigenvalues of elliptic operators in Sobolev extension domains

被引：0

作者：

Gol'dshtein, Vladimir ^{[1
]}

Pchelintsev, Valerii ^{[2
]}

Ukhlov, Alexander ^{[1
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, POB 653, IL-8410501 Beer Sheva, Israel

[2] Tomsk State Univ, Dept Math Anal & Theory Funct, Lenin Ave 36, Tomsk 634050, Russia

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2024年 / 14卷 / 03期

关键词：

Elliptic equations; Sobolev spaces; Extension operators; QUASI-CONFORMAL MAPPINGS; LAPLACIANS; SPACES;

D O I：

10.1007/s13324-024-00926-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain estimates of Neumann eigenvalues of the divergence form elliptic operators in Sobolev extension domains. The suggested approach is based on connections between divergence form elliptic operators and quasiconformal mappings. The connection between Neumann eigenvalues of elliptic operators and the smallest-circle problem (initially suggested by J. J. Sylvester in 1857) is given.

引用

页数：16

共 30 条

[1]

Ahlfors LV., 1966, LECT QUASICONFORMAL

[2]

Ashbaugh M.S., 1999, London Math. Soc. Lecture Note Ser., V273, P95

[3] UNIVERSAL BOUNDS FOR THE LOW EIGENVALUES OF NEUMANN LAPLACIANS IN N-DIMENSIONS [J].