Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space

被引：7

作者：

Magnanini, Rolando ^{[1
]}

Sakaguchi, Shigeru ^{[2
]}

机构：

[1] Univ Florence, Dipartimento Matemat U Dini, I-50134 Florence, Italy

[2] Hiroshima Univ, Grad Sch Engn, Dept Appl Math, Higashihiroshima 7398527, Japan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 248卷 / 05期

基金：

日本学术振兴会;

关键词：

Heat equation; Overdetermined problems; Stationary isothermic surfaces; Hyperplanes; Monge-Ampere-type equation;

D O I：

10.1016/j.jde.2009.11.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the entire graph S of a continuous real function over R(N-1) with N >= 3. Let Omega be a domain in R(N) with S as a boundary. Consider in Omega the beat now with initial temperature 0 and boundary temperature 1. The problem we consider is to characterize S in such a way that there exists a stationary isothermic surface in Omega. We show that S must be a hyperplane under some general conditions on S. This is related to Liouville or Bernstein-type theorems for some elliptic Monge-Ampere-type equation. (c) 2009 Elsevier Inc. All rights reserved.

引用

页码：1112 / 1119

页数：8

共 50 条

[41] IMMERSION OF LOBACHEVSKIAN N-DIMENSIONAL SPACES INTO EUCLIDEAN (2N-1)-DIMENSIONAL SPACE
AMINOV, YA
DOKLADY AKADEMII NAUK SSSR, 1977, 236 (03): : 521 - 524
[42] COULOMB GREENS-FUNCTIONS, IN AN N-DIMENSIONAL EUCLIDEAN-SPACE
CHETOUANI, L
HAMMANN, TF
JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (12) : 2944 - 2948
[43] On superintegrable symmetry-breaking potentials in N-dimensional Euclidean space
Kalnins, EG
Williams, GC
Miller, W
Pogosyan, GS
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2002, 35 (22): : 4755 - 4773
[44] A design of modulation with the same distance constellation in n-dimensional Euclidean space
Kohri, T
Hattori, T
VTC2004-FALL: 2004 IEEE 60TH VEHICULAR TECHNOLOGY CONFERENCE, VOLS 1-7: WIRELESS TECHNOLOGIES FOR GLOBAL SECURITY, 2004, : 3885 - 3889
[45] On isotopic and discrete realizations of maps of an n-dimensional sphere in Euclidean space
Akhmetev, PM
SBORNIK MATHEMATICS, 1996, 187 (7-8) : 951 - 980
[46] MAXIMAL PACKING DENSITY OF N-DIMENSIONAL EUCLIDEAN SPACE WITH EQUAL BALLS
LEVENSHTEIN, VI
MATHEMATICAL NOTES, 1975, 18 (1-2) : 765 - 771
[47] N-Dimensional Approximation of Euclidean Distance
Cardarilli, Gian Carlo
Di Nunzio, Luca
Fazzolari, Rocco
Nannarelli, Alberto
Re, Marco
Spano, Sergio
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS, 2020, 67 (03) : 565 - 569
[48] SOME REMARKS ON SURFACES IN 4-DIMENSIONAL EUCLIDEAN SPACE
BURES, J
CZECHOSLOVAK MATHEMATICAL JOURNAL, 1975, 25 (03) : 480 - 490
[49] A characteristic feature of the n-dimensional sphere in the Euclidean space E(n+p)
Bodrenko, II
RUSSIAN ACADEMY OF SCIENCES SBORNIK MATHEMATICS, 1995, 83 (02) : 315 - 320
[50] GENERALIZED OSCULATING CURVES OF TYPE (n-3) IN THE n-DIMENSIONAL EUCLIDEAN SPACE
Bektas, Ozcan
Bekiryazici, Zafer
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2022, 71 (01): : 212 - 225

← 1 2 3 4 5 →