A QUANTITATIVE SECOND ORDER MINIMALITY CRITERION FOR CAVITIES IN ELASTIC BODIES

被引：11

作者：

Capriani, Giuseppe Maria ^{[1
]}

Julin, Vesa ^{[1
]}

Pisante, Giovanni ^{[2
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Cacciopoli, I-80126 Naples, Italy

[2] Univ Naples 2, Dipartimento Matemat, I-81100 Caserta, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2013年 / 45卷 / 03期

关键词：

calculus of variations; second order minimality conditions; free discontinuity problems; STRAINED CRYSTALLINE FILMS; SURFACE-DIFFUSION; ENERGY; INSTABILITY; EVOLUTION; MODEL;

D O I：

10.1137/120872152

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a functional which models an elastic body with a cavity. We show that if a critical point has positive second variation, then it is a strict local minimizer. We also provide a quantitative estimate.

引用

页码：1952 / 1991

页数：40

共 20 条

[1]

Acerbi E, COMM MATH P IN PRESS

[2] ESTIMATES NEAR BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .2. [J].

AGMON, S ;

DOUGLIS, A ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1964, 17 (01) :35-&

[3]

Ambrosio L., 2004, OXFORD LECT SER MATH, V25

[4] INTERFACE MORPHOLOGY DEVELOPMENT DURING STRESS-CORROSION CRACKING .1. VIA SURFACE DIFFUSION [J].

ASARO, RJ ;

TILLER, WA .

METALLURGICAL TRANSACTIONS, 1972, 3 (07) :1789-&

[5] Computing the equilibrium configuration of epitaxially strained crystalline films [J].

Bonnetier, E ;

Chambolle, A .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2002, 62 (04) :1093-1121

[6]

Bonnetier E, 1999, RAIRO-MATH MODEL NUM, V33, P573

[7] A second order minimality condition for the Mumford-Shah functional [J].

Cagnetti, F. ;

Mora, M. G. ;

Morini, M. .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2008, 33 (01) :37-74

[8] A Selection Principle for the Sharp Quantitative Isoperimetric Inequality [J].

Cicalese, Marco ;

Leonardi, Gian Paolo .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2012, 206 (02) :617-643

[9] Nonlinear effects of the stress driven rearrangement instability of solid free surfaces [J].

Colin, J ;

Grilhé, J .

JOURNAL OF ELASTICITY, 2004, 77 (03) :177-185

[10] About stability of equilibrium shapes [J].

Dambrine, M ;

Pierre, M .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2000, 34 (04) :811-834

← 1 2 →