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A characterization of elliptic operators

Grzegorz Łysik, Paweł M. Wójcicki (2014)

Annales Polonici Mathematici

We give a characterization of constant coefficients elliptic operators in terms of estimates of their iterations on smooth functions.

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

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 Ω ⊂ ℝ2the functional is I ( u ) = 1 2 Ω - 1 | 1 - | D u | 2 | 2 + | D 2 u | 2 d z I ϵ ( u ) = 1 2 ∫ Ω ϵ -1 1 − Du 2 2 + ϵ D 2 u 2 d z whereubelongs to the subset of functions in W 0 2 , 2 ( Ω ) W02,2(Ω) whose gradient (in the sense of trace) satisfiesDu(x)·ηx = 1 where ηx is the inward pointing unit normal to ∂Ω at x. In [Ann. Sc. Norm. Super. Pisa Cl....

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

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 Ω ⊂ ℝ2 the functional is I ϵ ( u ) = 1 2 Ω ϵ -1 1 Du 2 2 + ϵ D 2 u 2 d z where u belongs to the subset of functions in W 0 2 , 2 ( Ω ) whose gradient (in the sense of trace) satisfies Du(x)·ηx = 1 where ηx is the inward pointing unit normal ...

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