TITLE

# Differentiability and higher integrability results for local minimizers of splitting-type variational integrals in 2D with applications to nonlinear Hencky-materials

AUTHOR(S)
Bildhauer, Michael; Fuchs, Martin
PUB. DATE
January 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Jan2010, Vol. 37 Issue 1/2, p167
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We prove higher integrability and differentiability results for local minimizers u: $${\mathbb {R}^2\supset\Omega\to\mathbb {R}^M}$$, M = 1, of the splitting-type energy $${\int_{\Omega}[h_1(|\partial_1 u|)+h_2(|\partial_2 u|)]\,{\rm d}x}$$ . Here h1, h2 are rather general N-functions and no relation between h1 and h2 is required. The methods also apply to local minimizers u: $${\mathbb {R}^2\supset\Omega \to \mathbb {R}^2}$$ of the functional $${\int_{\Omega}[h_1(|{\rm div}\,{\rm u}|)+h_2(|\varepsilon^D(u)|)]\,{\rm d}x}$$ so that we can include some variants of so-called nonlinear Hencky-materials. Further extensions concern non-autonomous problems.
ACCESSION #
45391245

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