The effect of a penalty term involving higher order derivatives on the distribution of phases in an elastic medium with a two-well elastic potential

✍ Scribed by M. Bildhauer; M. Fuchs; V. G. Osmolovskii

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 173 KB
• Volume: 25
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.287

✦ Synopsis

Abstract

We consider the problem of minimizing

0<p<1, h∈ℝ, σ>0, among functions u:ℝ^d^⊃Ω→ℝ^d^, u~∣∂Ω~=0, and measurable characteristic functions χ:Ω→ℝ. Here ƒ^+^~h~, ƒ^−^, denote quadratic potentials defined on the space of all symmetric d×d matrices, h is the minimum energy of ƒ^+^~h~ and ε(u) denotes the symmetric gradient of the displacement field. An equilibrium state û, χˆ, of I [·,·,h, σ] is termed one‐phase if χˆ≡0 or χˆ≡1, two‐phase otherwise. We investigate the way in which the distribution of phases is affected by the choice of the parameters h and σ. Copyright 2002 John Wiley & Sons, Ltd.