A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity
Andrew Lorent (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain ⊂ ℝthe functional is I ϵ ( u ) = 1 2 ∫ Ω ϵ -1 1 − Du 2 2 + ϵ D 2 u 2 d z wherebelongs to the subset of functions in W02,2(Ω) whose gradient (in the sense of trace) satisfies()· = 1 where is the inward pointing unit normal to at . In [1...