## P. Bousquet - L. Brasco - V. Julin

# Lipschitz regularity for local minimizers of some widely degenerate problems

created by brasco on 04 Sep 2014

modified on 05 Aug 2015

[BibTeX]

*Accepted Paper*

**Inserted:** 4 sep 2014

**Last Updated:** 5 aug 2015

**Journal:** Ann. Sc. Norm. Super. Pisa Cl. Sci.

**Pages:** 29

**Year:** 2014

**Abstract:**

We consider local minimizers of the functional
\[
\sum_{i=1}^N \int (\vert u_{x_i}\vert-\delta_i)^p_+\, dx+\int f\, u\, dx,
\]
where $\delta_1,\dots,\delta_N\ge 0$ and $(\,\cdot\,)_+$ stands for the positive part.
Under suitable assumptions on $f$, we prove that local minimizers are Lipschitz continuous functions if $N=2$ and $p\ge 2$, or if $N\ge 2$ and $p\ge 4$.

**Keywords:**
Degenerate elliptic equations, Lipschitz regularity, Anisotropic problems

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