*Published Paper*

**Inserted:** 9 dec 2005

**Journal:** Asympt. Anal.

**Volume:** 44

**Pages:** 221-235

**Year:** 2005

**Abstract:**

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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