A quantitative second order minimality criterion for cavities in elastic bodies

2011/12/12 by Giuseppe Maria Capriani, Capriani, Giuseppe Maria, Vesa Julin +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP #math.OC #msc:49Q20 #msc:74G40 #msc:74G55 #msc:74G65

paper · pdf · doi:10.48550/arxiv.1112.2482

Accepted Paper, SIAM J. Math. Anal

arxiv created 2013/04/04 · arxiv updated 2013/04/05

Abstract

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.

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