Line energies for gradient vector fields in the plane

被引：86

作者：

Ambrosio, L ^{[1
]}

De Lellis, C ^{[1
]}

Mantegazza, C ^{[1
]}

机构：

[1] Scuola Normale Super Pisa, I-56100 Pisa, Italy

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 1999年 / 9卷 / 04期

关键词：

D O I：

10.1007/s005260050144

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the singular perturbation of integral(1 - \del u\(2))(2) by epsilon(2)\del(2)u\(2). This problem, which could be thought as the natural second order version of the classical singular perturbation of the potential energy integral(1 - u(2))(2) by epsilon(2)\del(2)u\(2), leads, as in the first order case, to energy concentration effects on hypersurfaces. In the two dimensional case we study the natural domain for the limiting energy and prove a compactness theorem in this class.

引用

页码：327 / 355

页数：29

共 21 条

[1] RANK ONE PROPERTY FOR DERIVATIVES OF FUNCTIONS WITH BOUNDED VARIATION [J].