Regularity for energy-minimizing area-preserving deformations

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Abstract / Description of output

In this paper we establish the square integrability of the nonnegative hydrostatic pressure p, that emerges in the minimization problem
infK∫Ω|∇v|2,Ω⊂R2
as the Lagrange multiplier corresponding to the incompressibility constraint det∇v=1 a.e. in Ω. Our method employs the Euler-Lagrange equation for the mollified Cauchy stress C satisfied in the image domain Ω⋆=u(Ω). This allows to construct a convex function ψ, defined in the image domain, such that the measure of the normal mapping of ψ controls the L2 norm of the pressure. As a by-product we conclude that u∈C12loc(Ω) if the dual pressure (introduced in Karakhanyan, Manuscr. Math. 138:463, 2012) is nonnegative.
Original languageEnglish
Pages (from-to)213-223
Number of pages11
JournalJournal of Elasticity
Volume114
Issue number2
Early online date28 Mar 2013
DOIs
Publication statusPublished - Feb 2014

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