# Regularity results via duality for minimizers of degenerate functionals

created by passarell on 09 Dec 2005

[BibTeX]

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 $\lambda$.