Asymptotics of solutions to the Laplace-Beltrami equation on a rotation surface with a cusp

被引：1

作者：

Kiselev, O. ^{[1
]}

Shestakov, I. ^{[2
]}

机构：

[1] Ctr Comp, Inst Math, Dept Differential Equat, Ufa, Russia

[2] Univ Potsdam, Inst Math, Potsdam, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 362卷 / 02期

关键词：

Manifolds with singularities; Laplace-Beltrami operator;

D O I：

10.1016/j.jmaa.2009.08.039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we study an asymptotic behaviour of solutions to the Laplace-Beltrami operator on a rotation surface near a cuspidal point. To this end we use the WKB-approximation. This approach describes the asymptotic behaviour of the solution more explicitly than abstract theory for operators with operator-valued coefficients. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：393 / 400

页数：8

共 50 条

[11] ON THE RESOLVENT OF THE LAPLACE-BELTRAMI OPERATOR IN HYPERBOLIC SPACE [J].

Guseinov, Gusein Sh. .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2015, 99 (02) :186-206

[12] Anisotropic Laplace-Beltrami Operators for Shape Analysis [J].

Andreux, Mathieu ;

Rodola, Emanuele ;

Aubry, Mathieu ;

Cremers, Daniel .

COMPUTER VISION - ECCV 2014 WORKSHOPS, PT IV, 2015, 8928 :299-312

[13] Mean Laplace-Beltrami Operator for Quadrilateral Meshes [J].

Xiong, Yunhui ;

Li, Guiqing ;

Han, Guoqiang .

TRANSACTIONS ON EDUTAINMENT V, 2011, 6530 :189-201

[14] ON THE LAPLACE-BELTRAMI OPERATOR ON COMPACT COMPLEX SPACES [J].

Bei, Francesco .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (12) :8477-8505

[15] Shape sensitivity for the Laplace-Beltrami operator with singularities [J].

Ferchichi, J ;

Zolésio, JP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 196 (02) :340-384

[16] Statistical Properties of Eigenvalues of Laplace-Beltrami Operators [J].

Jiang, Tiefeng ;

Wang, Ke .

JOURNAL OF THEORETICAL PROBABILITY, 2021, 34 (03) :1061-1109

[17] Laplace-Beltrami Differentiability of Positive Definite Kernels on the Sphere [J].

M. H. CASTRO ;

V. A. MENEGATTO ;

C. P. OLIVEIRA .

Acta Mathematica Sinica,English Series, 2013, (01) :93-104

[18] The Hierarchical Subspace Iteration Method for Laplace-Beltrami Eigenproblems [J].

Nasikun, Ahmad ;

Hildebrandt, Klaus .

ACM TRANSACTIONS ON GRAPHICS, 2022, 41 (02)

[19] On the eigenfunction expansion of the Laplace-Beltrami operator in hyperbolic space [J].

Guseinov, Gusein Sh. .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2015, 60 (10) :1309-1326

[20] Laplace-Beltrami differentiability of positive definite kernels on the sphere [J].

M. H. Castro ;

V. A. Menegatto ;

C. P. Oliveira .

Acta Mathematica Sinica, English Series, 2013, 29 :93-104

← 1 2 3 4 5 →