Calculus of Variations and Geometric Measure Theory
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M. Carozza - G. Moscariello - A. Passarelli di Napoli

Regularity results via duality for minimizers of degenerate functionals

created by passarell on 09 Dec 2005


Published Paper

Inserted: 9 dec 2005

Journal: Asympt. Anal.
Volume: 44
Pages: 221-235
Year: 2005


We prove a regularity result for local minimizers of degenerate variational integrals, whose model arises in the study of mappings with finite distortion.

The degeneracy function ${\cal K}(x)$ lies in the exponential class, i.e. $exp (\lambda {\cal K}(x)) $ is integrable for some $\lambda>0$.

The right space of the gradient of a local minimizer $u$ turns out to be the Zygmund class $L^p\log^{-1} L$. Our result states that if $\lambda$ is sufficiently large, then $Du$ belongs to the Zygmund space $L^p\log^\alpha L$, \ $\alpha\geq 1$ and $\alpha$ encreases with $\lambda$.

Keywords: degenerate variational integrals, duality theory, mappings with finite distortion


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