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
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
Issue number2
Early online date28 Mar 2013
Publication statusPublished - Feb 2014


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