A Payne-Rayner Type Inequality for the Robin Problem on Arbitrary Minimal Surfaces in RN

被引：0

作者：

Takahashi, Futoshi ^{[1
]}

Uegaki, Akinobu ^{[1
]}

机构：

[1] Osaka City Univ, Dept Math, Sumiyoshi Ku, Osaka 5588585, Japan

来源：

RESULTS IN MATHEMATICS | 2011年 / 59卷 / 1-2期

关键词：

Robin problem; Payne-Rayner type inequality; ISOPERIMETRIC INEQUALITY;

D O I：

10.1007/s00025-010-0064-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a Payne-Rayner type inequality for the first eigenfunction of the Laplacian with Robin boundary condition on any compact minimal surface with boundary in R-N. We emphasize that no topological condition is necessary on the boundary.

引用

页码：107 / 114

页数：8

共 27 条

[1] A GENERALIZATION OF THE PAYNE-RAYNER ISOPERIMETRIC INEQUALITY
MOSSINO, J
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1983, 2A (03): : 335 - 342
[2] 1ST EIGENFUNCTION OF A MEMBRANE - EXTENSION TO N DIMENSIONS OF PAYNE-RAYNER ISOPERIMETRIC INEQUALITY
KOHLERJOBIN, MT
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1977, 28 (06): : 1137 - 1140
[3] ISOPERIMETRIC MONOTONICITY AND ISOPERIMETRIC-INEQUALITIES OF PAYNE-RAYNER TYPE FOR THE 1ST EIGENFUNCTION OF THE HELMHOLTZ PROBLEM
KOHLERJOBIN, MT
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1981, 32 (06): : 625 - 646
[4] A Payne–Rayner Type Inequality for the Robin Problem on Arbitrary Minimal Surfaces in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^N}$$\end{document}
Futoshi Takahashi
Akinobu Uegaki
Results in Mathematics, 2011, 59 (1-2) : 107 - 114
[5] Complete minimal surfaces densely lying in arbitrary domains of Rn
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[6] Minimal Surfaces with Constraints of Inequality Type
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RUSSIAN MATHEMATICS, 2012, 56 (11) : 45 - 51
[7] Minimal surfaces with constraints of inequality type
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[8] Existence of proper minimal surfaces of arbitrary topological type
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[9] A Schwarz-type formula for minimal surfaces in Euclidean space Rn
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[10] PLATEAUS PROBLEM FOR EMBEDDED MINIMAL SURFACES OF THE TYPE OF THE DISK
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ARCHIV DER MATHEMATIK, 1978, 31 (04) : 374 - 381

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