Vector-Valued Local Minimizers of Nonconvex Variational Problems

On the competition of elastic energy and surface energy in discrete numerical schemes

“…As proved in [15] and [11], a curve σ that realises the infimum in the above expression is a geodesic with respect to this metric and the curve σ then realises an interfacial layer with minimal energy…”

On reconstitutive phase transitions and the jump of the chemical potential

“…two solutions to (7.4). Equation (7.14) implies 2θW(χ 0 ) = (∂ u χ 0 ) 2 , and after reparametrisation we obtain, see [28] for details,…”

“…To analyse the conditions (7.12), (7.13) near the interface we follow Sternberg [28] and multiply (7.12) by ∂ u χ 0 . Integration from u = −∞ to u = +∞ yields…”

Cahn–Hilliard equations incorporating elasticity: analysis and comparison to experiments

“…We name here the generalization to multiple phases [32]; to non-isothermal settings [33,34]; to concentrationdependent mobilities [35]; the incorporation of convective [36] and viscous effects [37,38]; the coupling to the Navier-Stokes equations [39,40]; and the derivation of a general CH/AllenCahn model [41]. The sharp interface limit of the CH model (and its extensions) is also well understood [42][43][44]. Besides a classification of the different models, this resulted in a better understanding of surface tension and the role of the Gibbs-Thomson law [45].…”