A BERNSTEIN RESULT FOR ENERGY MINIMIZING HYPERSURFACES

被引：15

作者：

DIERKES, U ^{[1
]}

机构：

[1] UNIV BONN,INST ANGEW MATH,W-5300 BONN 1,GERMANY

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 1993年 / 1卷 / 01期

关键词：

D O I：

10.1007/BF02163263

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that there are no entire, positive, stable solutions in R(n) of the Euler equation corresponding to the singular variational integral integral u(alpha) square-root 1+\Du\2 dx, alpha > 0, if alpha + n < 5.236.... Furthermore we prove a related result for smooth boundaries of least alpha-energy integral \x(n+1)\alpha\Dphi(U)\ in R(n+1).

引用

页码：37 / 54

页数：18

共 33 条

[1] SOME INTERIOR REGULARITY THEOREMS FOR MINIMAL SURFACES AND AN EXTENSION OF BERNSTEINS THEOREM [J].

ALMGREN, FJ .

ANNALS OF MATHEMATICS, 1966, 84 (02) :277-&

[2]

[Anonymous], 1983, ELLIPTIC PARTIAL DIF

[3]

BEMELMANS J, 1987, ARCH RATION MECH AN, V100, P838

[4]

Bernstein S., 1914, COMM SOC MATH KHARKO, V15, P38

[5]

BOHME R, 1980, PAC J MATH, V88, P247

[6] MINIMAL CONES AND BERNSTEIN PROBLEM [J].

BOMBIERI, E ;

DEGIORGI, E ;

GIUSTI, E .

INVENTIONES MATHEMATICAE, 1969, 7 (03) :243-&

[7]

CAFFARELLI L, FORM BERNSTEINS THEO

[8] COMPLETE MINIMAL SURFACES IN EUCLIDEAN N-SPACE [J].

CHERN, SS ;

OSSERMAN, R .

JOURNAL D ANALYSE MATHEMATIQUE, 1967, 19 :15-&

[9]

De Giorgi E., 1965, ANN SCUOLA NORM SUP, V19, P79

[10] ON THE NONEXISTENCE OF ENERGY STABLE MINIMAL CONES [J].

DIERKES, U .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1990, 7 (06) :589-601

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